Question

Add$\frac{5}{3w-2}+\frac{2}{w+1}$.

Short answer

The sum is$\frac{11w+1}{(3w-2)(w+1)}$.

Step-by-step solution

Given Information

The Given expression is$\frac{5}{3w-2}+\frac{2}{w+1}$.

Find the LCD of denominators.

Since there are no common factors in denominators.

The LCD is$(3w-2)(w+1)$.

Rewrite each fraction as an equivalent fraction with the LCD.

$=\frac{5(w+1)}{(3w-2)(w+1)}+\frac{2(3w-2)}{(3w-2)(w+1)}$

Simplify numerator.

$=\frac{5w+5}{(3w-2)(w+1)}+\frac{6w-4}{(3w-2)(w+1)}$

Add and simplify the numerator.

Take common denominator.

$=\frac{5w+5+6w-4}{(3w-2)(w+1)}$

$=\frac{11w+1}{(3w-2)(w+1)}$