Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 11 - Rational Expressions and Functions - 11-1 Simplifying Rational Expressions - Practice and Problem-Solving Exercises - Page 656: 37


$-\frac{2a+1}{a+3}$ $a\ne\frac{5}{2}$ and $a \ne -3$

Work Step by Step

To simplify the expression, we need to arrange the numerator and denominator in descending powers and then factor the numerator and denominator. $\frac{4a^2 - 8a - 5}{15 - a - 2a^2}$ = $\frac{4a^2 - 8a - 5}{-2a^2 - a +15}$ Now we need to factor out a negative from the denominator and then factor: $-\frac{4a^2 - 8a - 5}{2a^2 + a -15}$ = $-\frac{(2a+1)(2a-5)}{(2a-5)(a+3)}$ Now we can divide out the common factor of $(2a-5)$ $-\frac{(2a+1)(2a-5)}{(2a-5)(a+3)} = -\frac{2a+1}{a+3}$ To find the excluded values, we need to look at the factored expression before simplifying: $-\frac{(2a+1)(2a-5)}{(2a-5)(a+3)}$ Setting each factor of the denominator equal to 0, we will find the excluded values: $2a - 5 = 0$ $2a=5$ $a=\frac{5}{2}$ $a+3 = 0$ $a = -3$ Therefore, $a\ne\frac{5}{2}$ and $a \ne -3$
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