If $\frac{2x + 6} {(x + 2)^2}- \frac{2} {x + 2} = \frac{a} {(x + 2)^2}$, then what is $a$? $$\frac{2x + 6} {(x + 2)^2}- \frac{2} {x + 2}$$
The expression above is equivalent to $$\frac{a} {(x + 2)^2}$$
where $a$ is a positive constant and $x \neq -2$.
What's the value of $a$?

There is no need to do any algebra.
Consider
$$
\frac{2x + 6} {(x + 2)^2}- \frac{2} {x + 2}
=
\frac{a} {(x + 2)^2}
$$
Since this equality holds for all values of $x\ne -2$,
set $x=0$ and get
$$
\frac{6} {2^2}- \frac{2} {2}
=
\frac{a} {2^2}
$$
which gives $a=2$.
