Splitting fractions with a linear denominator: $\frac{2x-1}{x+2}$ How can $$\frac{2x-1}{x+2}$$ be split to give $$A-\frac{B}{x+2}$$
where $A$ and $B$ are integers?
The solution is $$2-\frac{5}{x+2}.$$

Observe that if you set 
$$y=x+2,\quad x=y-2,$$ then you get
$$
\frac{2x-1}{x+2}=\frac{2(y-2)-1}{y}=\frac{2y-5}{y}=2-\frac{5}{y}=2-\frac{5}{x+2}
$$ as wanted.
