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: 38


$\frac{3m+4}{m-7}$ $m \ne\ 7$ and $m \ne -4$

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. $\frac{16 + 16m +3m^2}{m^2 - 3m - 28}$ = $\frac{3m^2+16m+16}{m^2 - 3m - 28}$ = $\frac{$(3m+4)(m+4}{(m-7)(m+4)}$ Now we can divide out the common factor of $(m+4)$ $\frac{(3m+4)(m+4}{(m-7)(m+4)}$ = $\frac{3m+4}{m-7}$ To find the excluded values, we need to look at the factored expression before simplifying: $\frac{$(3m+4)(m+4}{(m-7)(m+4)}$ Setting each factor of the denominator equal to 0, we will find the excluded values: $m-7 = 0$ $m=7$ $m+4 = 0$ $m = -4$ Therefore, $m \ne\ 7$ and $m \ne -4$
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