Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Review - Concept Check - Page 132: 14

Answer

A) How to multiply and divide rational expression. In the case of multiplication you should factor so you would be able to identify similar terms in the numerator and the denonminator and eliminate them. CLARIFICATION Only eliminate the factors that are in the numerator and also in the denominator. $$(\frac{C(a-b)}{D(f-e)})(\frac{K(m-l)}{T(a-b)})$$ In this case you wil eliminate (a-b). In the division first you should switch the numerator and denominator of one term. Then factor them to simplify it. $$(\frac{K(m-l)}{D(f-e)}) \div(\frac{K(m-l)}{T(a-b)})$$ Now switch them. $$(\frac{K(m-l)}{D(f-e)}) \div(\frac{T(a-b)}{K(m-l)})$$ In this case you can eliminate K(m-l) and have your answer. B) How to add and subtract rational expressions. Normally you need to find the LCD. Sometimes it is a little bit hard so all you have to do is to multiply all the denominators and you will find it. C) What LCD do we use to perform the addition in the expression $(\frac{3}{x-1})+(\frac{5}{x+2})$. So we should multiply each numerator with the numerator of the apposite term. $$\frac{3(x+2)+5(x-1)}{(x+2)(x-1)}$$ $$\frac{3x+6+5x-5}{(x+2)(x-1)}$$ $$\frac{8x+1}{(x+2)(x-1)}$$

Work Step by Step

A) How to multiply and divide rational expression. In the case of multiplication you should factor so you would be able to identify similar terms in the numerator and the denonminator and eliminate them. CLARIFICATION Only eliminate the factors that are in the numerator and also in the denominator. $$(\frac{C(a-b)}{D(f-e)})(\frac{K(m-l)}{T(a-b)})$$ In this case you wil eliminate (a-b). In the division first you should switch the numerator and denominator of one term. Then factor them to simplify it. $$(\frac{K(m-l)}{D(f-e)}) \div(\frac{K(m-l)}{T(a-b)})$$ Now switch them. $$(\frac{K(m-l)}{D(f-e)}) \div(\frac{T(a-b)}{K(m-l)})$$ In this case you can eliminate K(m-l) and have your answer. B) How to add and subtract rational expressions. Normally you need to find the LCD. Sometimes it is a little bit hard so all you have to do is to multiply all the denominators and you will find it. C) What LCD do we use to perform the addition in the expression $(\frac{3}{x-1})+(\frac{5}{x+2})$. So we should multiply each numerator with the numerator of the apposite term. $$\frac{3(x+2)+5(x-1)}{(x+2)(x-1)}$$ $$\frac{3x+6+5x-5}{(x+2)(x-1)}$$ $$\frac{8x+1}{(x+2)(x-1)}$$
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