Hi,

I am just curious about how to prove these following things:

Firstly, what's the proof for the following:

$\displaystyle

\frac{8x+7}{(2x+1)^2} = \frac{a}{(2x+1)^2} + \frac{b}{2x+1}$

I was also told that the polynomial in the numerator should be 1 degree lower than the one in the denominator - why?

Also, I was wondering.

$\displaystyle

y^2 = 3x - 12$ why does that become

$\displaystyle y = +\sqrt[2]{3x-12}\ or -\sqrt[2]{3x-12}$

Again, I'm looking for a proof explanation so that I can remember it and derive it if I forget.

Thanks!