Is $\frac{\frac{1}{b}-\frac{1}{2}}{b-2}$ the same as $\frac{\frac{2-b}{2b}}{b-2}$? Have I subtracted 2 fractions correctly?
$\frac{\frac{1}{b}-\frac{1}{2}}{b-2}$
Starting with the numerator which is a difference of fractions, the least common denominator is 2b? So:
$\frac{2(1)}{2b}-\frac{b(1)}{2b}$ = $\frac{2}{2b}-\frac{b}{2b}$ = $\frac{2-b}{2b}$
So my newly simplified expression is:
$\frac{\frac{2-b}{2b}}{b-2}$
My question - is this correct? If yes, great - now how would I go about simplifying further by taking the denominator $b-2$ into account? If no, where did I go wrong?

It is correct, since $$\frac{1}{b}-\frac{1}{2}=\frac{2}{2b}-\frac{b}{2b}=\frac{2-b}{2b}$$
