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 655: 18


$a\ne -1$ $\frac{a+1}{5}$

Work Step by Step

To find excluded values, we look at the denominator and find the values that would make it zero. To do this, we can set the denominator equal to zero and solve. $5a + 5 = 0$ $5a +5=0 -5$ Subtract 5 from each side $\frac{5}{5}a = \frac{-5}{5}$ Divide each side by 5 $a = -1$ Simplify Therefore, $a\ne-1$, therefore -1 is our excluded value. To simplify the expression, we need to factor the numerator and denominator. $\frac{a^2+2a+1}{5a+5} = \frac{(a+1)(a+1)}{5(a+1)}$ Now we can divide out the common factor of $(a+1)$ $\frac{(a+1)(a+1)}{5(a+1)} = \frac{a+1}{5}$
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