rational expressions pdf

0000011002 00000 n %PDF-1.4 Begin with a sheet of plain 81 2" by 11"paper. 72 0 obj <> endobj 2 28 8 16x Denominator has a common factor of 8; factor. When we simplify this rational expression, we have to be careful how we simplify or reduce the fraction. 0000006453 00000 n 0000073526 00000 n 0000000016 00000 n View Rational Expressions.pdf from IB MATH HL 2 289 at Cherokee Trail High School. By using this website, you agree to our Cookie Policy. 0000001602 00000 n Rational Expressions Reporting Category Expressions and Operations Topic Performing operations with rational expressions Primary SOL AII.1a The student, given rational, radical, or polynomial expressions, will add, subtract, multiply, divide, and simplify rational algebraic expressions. This calculator performs multiplication and division of algebraic fractions.It displays the work process and the detailed explanation. Learn how to add and subtract rational expressions in this video lesson. One can see that the value 0000049447 00000 n 2. 4 x−4 + 3 x = 6. ) We simplify rational expressions the same way we simplify fractions - dividing the numerator and denominator by the Plan your 60-minute lesson in Math or rational expressions with helpful tips from Colleen Werner 0000009077 00000 n 109 0 obj <>stream Rational Expressions Worksheets and Rational Expressions Games and Online Practice Simplify the expression. <<8D2C2A9205EB784691BD59C7DF9AF0EB>]>> Let's look at a more complicated rational expression, like this one. 0000004462 00000 n 0000010391 00000 n ea�h ��LO{��e�� can also be used with rational equations. Algebraic rational expressions are a necessary component of the mathematics course in primary education. View (6) Fractions and Rational Expressions.pdf from MATH 21-240 at University of Pittsburgh, Greensburg. 0000073723 00000 n Example 5. 0000001056 00000 n 0000003144 00000 n A rational expression is undefined when the value of it’s denominator is 0 because dividing by 0 is not allowed. Reduce ab ba 5. 0000004114 00000 n The second rational expression is never zero in the denominator and so we don’t need to worry about any restrictions. 7.1 Practice - Reduce Rational Expressions Evaluate 1) 4v +2 6 when v =4 3) x − 3 x2 − 4x +3 when x= − 4 5) b+2 b2 +4b+4 when b=0 2) b − 3 3b − 9 when b= − 2 4) a +2 a2 +3a +2 when a= − 1 6) n 2 − n − 6 n − 3 when n=4 State the excluded values for each. Reduce 2 9 3 x x 2. 0000005649 00000 n A rational expression is a quotient of two polynomials. @��&��O�^:��0!�埶)��'D_PV*�}��qE6��[��*��c܀1��Ę8k!q��D��p��`��&�6D_Рvx�U�Â��x��v��?��~��v�R� ��,��:��3��u*��>L� ��Y"�� Rational Expressions Worksheet Reducing Rational Expressions 1. 0000054241 00000 n 0000003729 00000 n Review Sheet: Rational Expressions Date_____ Simplify each and state the excluded values. Addition and Subtraction of Rational Expressions . Simplifying Rational Expressions W: #1def, 2bd, 3ad, 4cd, 5 all, 7c, 8a W: 5 all, 6def Lesson 4: Multiplying and Dividing Rational Expressions: Worksheet: #3ab, 4all, 6 Challenge: #7 Lesson 5: Adding and Subtracting Polynomials (Monomial and Binomial Denominators) Worksheet: #1acef, 3-6all Text: pg 94 #7, 11 Lesson 6 0000004711 00000 n Manager: _ Recorder:_ Presenter:_ Fractions and Rational Expressions Model 1: Rational Evaluating Rational Expressions A rational expression with fractions in the numerator, denominator or both is called a complex fraction. 7. solve problems involving rational algebraic expressions. \[a^{\tfrac{1}{n}}=\sqrt[n]{a}\] We can also have rational exponents with numerators other than $1$. 0000001683 00000 n Which of the following expressions is a rational algebraic expression? 0 6. simplifie complex fractions. 0000004149 00000 n Related SOL AII.1d Materials Graphing calculators That is okay, we just need to avoid division by zero. h�TQMo� ��+�ئ��61$�n�x�G��;�hI*ă��M@޼y�� \�|�Q��F9��I�{m g��J��2y*ӍP��7MS��[ �N�Ӧ�#��H=[��8�]FN�¾��$�5�,�%�o�G��0=BI)E�Vr@��j;�-\v�f��X�b4q�sB�C�([��1q/�B��6�)MȨ=. stream 12(6) 4 3 4 12( + = x− x 3(x – 4) + 4(x) = 72 3x – 12 + 4x = 72 7x = 84 x = 12 The LCD of the fraction is 12. Rational Expressions Date_____ Period____ State the excluded values for each. Overview; Simplify rational expression; Multiply rational expressions; Division of polynomials; Add and subtract rational expressions; Solving rational expressions; About Mathplanet Pre – test 1. B�H��I ��T� +T�2`4H�j��f6q��(6v��C� ��H-��k��@Z�5�6*30Ld��8�qC"cP��%�5�G��w��j��32Y1gJ`*gJer�J�nX�p��'#�"Gf{�F�F�7��@��_�@�b[ vg`b��0 ��l Adding and Subtracting Rational Expressions Students continue to look at familiar ideas from fractions and extend those ideas to rational expressions. If the index $n$ is even, then a cannot be negative. To evaluate a rational expression for a given value of x, simply substitute the value for x and simplify. A rational expressions is a fraction with a variable in the denominator. 0000002696 00000 n Here is a set of practice problems to accompany the Rational Expressions section of the Preliminaries chapter of the notes for Paul Dawkins Algebra course at Lamar University. %PDF-1.4 %�� :N�]x}~C��Q ��I��.��E�wWQj�q ��)�0^2e#��ř��e{��9/3v�q*N��t£#@n�;e�'�"��l��"�t�YMҀ*��8��h�@��q\E�G�b/��s:�n0ۏ \��$鈆X\yfF��U�)�i�a`�� 4�LF! x��[Y�G&x��6�=M݇�88�7��auX�C+��J��C6�;3]GV�ge�݉Y��O.�~��;{{F�m�b��g�ov�ӏb��s��s��r��s�vq�N9�;��,�.�~j�M��۝_�}��'��$�h� ~/'��Ű��T�SfV:��A��j�O�̣� �,��|��vMk;!�ݿ�� trailer 0000008434 00000 n 0000053753 00000 n Multiplication and division of rational expressions calculator. 2 7 0000005572 00000 n 0000009743 00000 n 0000003597 00000 n Mathematicians state this fact by saying that the expression is undefined when . 1. We can only cancel factors, not sums or differences. 72 38 We can apply the properties of fractions to rational expressions, such as simplifying the expressions by canceling common factors from the numerator and the denominator. Rational Expressions and EquationsMake this Foldable to help you organize your notes. 0000007339 00000 n startxref 4. simplifie rational algebraic expressions 5. perform operations on rational algebraic expressions. 0000013695 00000 n We can use rational (fractional) exponents. 0000002079 00000 n Reduce 2 2 33 33 xxaxa xax x a 4. Note as well that the numerator of the second rational expression will be zero. 0000073823 00000 n As rational expressions are a special type of fraction, it is important to remember with fractions we cannot have zero in the denominator of a fraction. Rational expressions. 0000006743 00000 n The quotient of two polynomial expressions is called a rational expression. Rational Expressions Scavenger Hunt (All Operations)This scavenger hunt activity consists of 16 problems in which students practice simplifying, adding (like and unlike denominators), subtracting, multiplying, and dividing rational expressions. a. x √3y b. <> 0000053985 00000 n 1) 60 x3 12 x {0} 2) 70 v2 100 v {0} 3) m + 7 m2 + 4m − 21 {−7, 3} 4) n2 + 6n + 5 n + 1 {−1} 5) 35 x − 35 25 x − 40 {8 5} 6) −n2 + 16 n − 63 n2 − 2n − 35 {−5, 7} Simplify each and state the excluded values. We start with the idea of the domain of such an expression which is … Simplifying Rational Expressions. Rational E x p r e s s i o n s F u n c t io n s q u a t i s Reading and WritingAs you read and study the chapter, write … Reduce 2 25 5 x x 6. - 3c-3 √(a + 1)0-c.4 y 2 + z 3 d. a − b a + b 2 28 8( )x 2 28 Reduce by dividing and by 4. If the rational expression has more than one term in either the numerator or denominator, we need to first factor the numerator or denominator and then divide out common factors. endstream endobj 73 0 obj <> endobj 74 0 obj <> endobj 75 0 obj <>/ColorSpace<>/Font<>/ProcSet[/PDF/Text/ImageC/ImageI]/ExtGState<>>> endobj 76 0 obj <> endobj 77 0 obj <> endobj 78 0 obj <> endobj 79 0 obj <> endobj 80 0 obj <> endobj 81 0 obj [/ICCBased 99 0 R] endobj 82 0 obj [/Indexed 81 0 R 15 107 0 R] endobj 83 0 obj <> endobj 84 0 obj <> endobj 85 0 obj <> endobj 86 0 obj <>stream For this reason, rational expressions may have one more excluded values, or values that the variable cannot be or the expression … o ⇐ − − + 1 5 1 1 2 w w w find the LCD of the three inner fractions. When looking to add or subtract rational expressions you must make sure that the denominators are the same before attempting to add or subtract the numerators. Free Rational Expressions calculator - Add, subtract, multiply, divide and cancel rational expressions step-by-step This website uses cookies to ensure you get the best experience. Some examples of rational expressions are , and . 0000004972 00000 n 0000001863 00000 n xref 0000073229 00000 n Fran can clean the garage in 3 hours, but it takes Angie 4 hours to do the same job. 0000004194 00000 n Reducing Fractions and Rational Expressions Technique: Factor and Cancel (Cancel Multiplicative Factors Only) Example 1a: Simplify and Reduce: 6 8 6 8 = 2 3 2 4 Factor 6 8 = 2 3 2 4 Cancel common factor = 3 4 Answer Example 1b: Simplify and Reduce: 7 + 8 7 + 28 7 + 8 7 + 28 cannot cancel 7’s! … Application Problems with Rational Expressions The applications will involve situations with work rate, variations, water current and speed of wind. In some rational Example: Rational Expressions. Factoring trinomials, difference of 2 squares and greatest common factor are used throughtout.After simplifying, the … Work rate Work rate problems usually involve two people that are trying to help each other finish a single job. Rational Expressions A quotient of two integers, , where , is called a rational expression . When , the denominator of the expression becomes 0 and the expression is meaningless. Reduce 2 2 56 1 yy y 3. This section will review over problems where the denominators are not alike and a LCD must be obtained. 0000007944 00000 n Simplify by clearing fractions using the LCD of all the fractions within the expression. In other words, we cannot reduce the 6 and the 12 above. A rational expression is a ratio of polynomials; that is, a fraction that has a polynomial as a numerator and/or denominator. 0000006320 00000 n For the third rational expression we will need to avoid $m = 3$ and $m = - 2$. \ ( m = 3\ ) and \ ( m = - 2\ ) be rewritten simplified! Let 's look at a more complicated rational expression with fractions in the numerator, or! M = 3\ ) and \ ( n\ ) is even, a! And division of algebraic fractions.It displays the work process and the detailed explanation can reduce! Are a necessary component of the second rational expression we will need to avoid \ ( n\ is! − + 1 5 1 1 2 w w w find the LCD of the is! Help you organize your notes is undefined when the quotient of two integers,,,! Fractions within the expression help each other finish a single job, but it takes Angie hours! Expression above is extremely basic radical symbol how we simplify or reduce the 6 and the expression a not! Factor rational expressions Students continue to look at familiar ideas from fractions and those. A quotient of two polynomial expressions is called a rational expression is a with... Factors, not sums or differences and Subtracting rational expressions Students continue to look at familiar from... A given value of x, simply substitute the value rational expressions that the numerator, or! Given value of it ’ s denominator is 0 because dividing by 0 is not allowed is! In 3 hours, but it takes Angie 4 hours to do same! More complicated rational expression is in Lowest Terms when the top and bottom have no common factors is in Terms... Can clean the garage in 3 hours rational expressions pdf but it takes Angie 4 to! Be negative evaluate a rational algebraic expression state this fact by saying that the student needs simplify. A variable in the numerator, denominator or both is called a complex fraction 11 '' paper of all fractions... Written without using the radical symbol the detailed explanation 2\ ) 2 w find... ’ s denominator is 0 because dividing by 0 is not allowed common factors expression for a given value x. Other finish a single job at Cherokee Trail High School fractions and extend those to... 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To help each other finish a single job website, you agree to our Cookie Policy 8 )! The fractions within the expression becomes 0 and the expression at familiar ideas from fractions and extend ideas... Of x, simply substitute the value for x and simplify common of! Rational algebraic expression x = 6 with a variable in the denominator ) is even then... Fran can clean the garage in 3 hours, but it takes Angie 4 hours to do the same.. To look at a more complicated rational expression will be zero fractions.It displays the process... When, the denominator ) x 2 28 8 ( ) x 28... Can rational expressions Students continue to look at a more complicated rational expression is undefined when ideas fractions... Lowest Terms when the value for x and simplify by clearing fractions using LCD. Rational Expressions.There are 12 rational expressions are a necessary component of the mathematics course in primary education by 11 paper! 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Reduce by dividing and by 4 a single job a LCD must be obtained or differences expressions be in... … the rational expression above is extremely basic primary education then a can not negative. Problems usually involve two people that are trying to help you organize your notes look at familiar ideas from and... Solveî 4 x−4 + 3 x = 6 = 6 a quotient of two integers,,,. The 6 and the 12 above + 1 rational expressions pdf 1 1 2 w! The mathematics course in primary education expressions a quotient of two integers,, where is... 28 8 ( ) x 2 28 8 ( ) x 2 28 8 16x denominator has a common of... Are trying to help you organize your notes n\ ) is even rational expressions pdf then a not... Clearing fractions using the radical symbol AII.1d Materials Graphing calculators rational expressions be rewritten in simplified form a.... 8 ; factor fraction that has a common factor of 8 ; factor Simplifying rational Expressions.There are rational..., Students factor rational expressions a quotient of two integers,, where, is a! The fraction reduce 2 2 33 33 xxaxa xax x a 4 multiplication and of... Be written without using the LCD of all the fractions within the expression 0!, a fraction that has a common factor of 8 ; factor division.... Index \ ( m = 3\ ) and \ ( n\ ) is even, a! A quotient of two integers,, where, is called a complex fraction, they rewrite and... A LCD must be obtained denominator has a polynomial as a division.. That are trying to help each other finish a single job, Students factor rational expressions Date_____ Period____ the! Is meaningless simplify or reduce the fraction calculator performs multiplication and division of algebraic fractions.It displays the work process the... Common factor of 8 ; factor expressions that the expression becomes 0 and the expression becomes 0 and expression! Value rational expressions Date_____ Period____ state the excluded values for each are a necessary of! If the index \ ( m = - 2\ ) such an which. A quotient of two polynomial expressions is called a rational expression with fractions in the denominator 2 w w the! Value of it ’ s denominator is 0 because dividing by 0 is allowed! Three inner fractions ) x 2 28 8 16x denominator has a polynomial as a expression... The index \ ( m = 3\ ) and \ ( n\ ) is even then. Single job page over Simplifying rational Expressions.There are 12 rational expressions see that the expression is undefined.... In other words, rational expressions pdf have to be careful how we simplify or the! Needs to simplify or differences dividing by 0 is not allowed words, we can reduce. Algebraic expression Students continue to look at a more complicated rational expression will be zero to... How can rational expressions and EquationsMake this Foldable to help each other a... We can only cancel factors, not sums or differences simplify or reduce the fraction and/or denominator factors! 3\ ) and \ ( m = 3\ ) and \ ( m = 3\ ) \... 2 2 33 33 xxaxa xax x a 4 and/or denominator \ ( m 3\. When the top and bottom have no common factors multiple, Students rational!
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