Answer
$\frac{1}{3(x+3)}$.
Work Step by Step
The given expression is
$=\frac{1}{x^2+8x+15}\div \frac{3}{x+5}$
Factor $x^2+8x+15$.
Rewrite the middle term $8x$ as $5x+3x$.
$=x^2+5x+3x+15$
Group terms.
$=(x^2+5x)+(3x+15)$
Factor each term.
$=x(x+5)+3(x+5)$
Factor out $(x+5)$.
$=(x+5)(x+3)$
Substitute the factor into the given expression.
$=\frac{1}{(x+5)(x+3)}\div \frac{3}{x+5}$
$=\frac{1}{(x+5)(x+3)}\times \frac{x+5}{3}$
Cancel common terms.
$=\frac{1}{3(x+3)}$.
