Answer
$\frac{2x+5}{(x+1)(x+2)}$
Work Step by Step
$\frac{3}{x+1}-\frac{1}{x+2}$
Find the lowest common denominator (i.e. $(x+2)(x+1)$) and adjust the fractions accordingly:
$=\frac{3\times (x+2)}{(x+1)(x+2)}-\frac{1\times (x+1)}{(x+1)(x+2)}$
Expand any brackets:
$=\frac{3x+6}{(x+1)(x+2)}-\frac{x+1}{(x+1)(x+2)}$
Combine the fractions:
$=\frac{3x+6-(x+1)}{(x+1)(x+2)}$
Expand the negative sign:
$=\frac{3x+6-x-1}{(x+1)(x+2)}$
Collect the like terms:
$=\frac{2x+5}{(x+1)(x+2)}$
