Answer
$\frac{1}{y(y+2)}; y \ne 0,-2;$
Work Step by Step
$\frac{y^{-1}- (y+2)^{-1}}{2}$
The given expression can be written as
$=\frac{\frac{1}{y}- \frac{1}{y+2}}{2}; y \ne 0,-2;$
Take LCD in the numerator
$=\frac{\frac{y+2-y}{y(y+2)}}{2}; y \ne 0,-2;$
$=\frac{\frac{2}{y(y+2)}}{2}; y \ne 0,-2;$
$ =\frac{2}{y(y+2)} \times \frac{1}{2}; y \ne 0,-2;$
Cross out common factor.
$= \frac{1}{y(y+2)}; y \ne 0,-2;$
