Answer
Answer = $\frac{1}{x + 6}$
Work Step by Step
$\frac{x + 6}{x^{2} + 12x + 36}$
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)