## Algebra: A Combined Approach (4th Edition)

Answer = $\frac{1}{x + 6}$
$\frac{x + 6}{x^{2} + 12x + 36}$ In the denominator $\Longrightarrow$ $x^{2} + 12x + 36$, $x^{2}$ = x$\cdot$x 36 = $6^{2}$ And middle term is 2(x)(6) = 12x Thus the denominator is a perfect square trinomial. Thus, $x^{2} + 12x + 36$ = x(x) + 2(x)(6) + 6(6) = $(x + 6)^{2}$ The rational expression is: $\frac{x + 6}{x^{2} + 12x + 36}$ = $\frac{x + 6}{(x + 6)^2}$ = $\frac{x + 6}{(x + 6)(x + 6)}$ = $\frac{1}{x + 6}$ ....(Since $\frac{x + 6}{x + 6}$ = 1)