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 $$2-\frac{5}{x+2}.$$

$$\frac{2x-1}{x+2}=\frac{2(x+2)-5}{x+2}=\frac{2(x+2)}{x+2}-\frac{5}{x+2}=2-\frac{5}{x+2}$$
