## Algebra 1

Published by Prentice Hall

# Chapter 11 - Rational Expressions and Functions - 11-4 Adding and Subtracting Rational Expressions - Practice and Problem-Solving Exercises - Page 676: 29

#### Answer

$\frac{(a+4)(a-3)}{(a+5)(a+3)}$

#### Work Step by Step

To solve: $\frac{a}{a+3} - \frac{4}{a+5}$, you will first need to make sure both fractions have common denominators. To do this, we normally must find the LCD, or the Least Common Multiple, by writing out each as products of prime factors. However, since looking at each denominator is sufficient to see that there are no common factors, the LCD is $(a+3)(a+5)$ Now\times we can rewrite the fractions using the new LCD we found and use them to subtract our numerators. $\frac{a}{a+3} - \frac{4}{a+5}$ = $\frac{a \times (a+5)}{(a+3) \times (a+5)} - \frac{4 \times (a+3)}{(a+5)\times(a+3)}$ = $\frac{a(a+5) - 4(a+3) }{(a+5)(a+3)}$ We need to now simplify the numerator by distributing and then factoring: $\frac{a^2+5a-4a-12}{(a+5)(a+3)}$ = $\frac{a^2 + a-12}{(a+5)(a+3)} = \frac{(a+4)(a-3)}{(a+5)(a+3)}$ Since there are no common factors between the numerator and denominator, this is our final answer.

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