Answer
a. $\frac{1}{y}$.
b. $\frac{6}{k+4}$.
Work Step by Step
a.
The given expression is
$=\frac{x}{x+y}\div \frac{xy}{x+y}$
$=\frac{x}{x+y}\times \frac{x+y}{xy}$
Divide out the common factors.
$=\frac{1}{y}$.
b.
The given expression is
$=\frac{4k+8}{6k-10}\div \frac{k^2+6k+8}{9k-15}$
Factor.
$=\frac{4(k+2)}{2(3k-5)}\div \frac{(k+4)(k+2)}{3(3k-5)}$
$=\frac{4(k+2)}{2(3k-5)}\times \frac{3(3k-5)}{(k+4)(k+2)}$
Divide out the common factors.
$=\frac{6}{k+4}$.
