Question

Add$\frac{4}{2x+5}+\frac{2}{x-1}$.

Short answer

The sum is$\frac{2(4x+3)}{(2x+5)(x-1)}$.

Step-by-step solution

Given Information

The Given expression is$\frac{4}{2x+5}+\frac{2}{x-1}$.

Find the LCD of denominators.

Since there are no common factors in denominators.

The LCD is$(2x+5)(x-1)$.

Rewrite each fraction as an equivalent fraction with the LCD.

$=\frac{4(x-1)}{(2x+5)(x-1)}+\frac{2(2x+5)}{(2x+5)(x-1)}$

Simplify numerator.

$=\frac{4x-4}{(2x+5)(x-1)}+\frac{4x+10}{(2x+5)(x-1)}$

Add and simplify the numerator. 

Take common denominator.

$=\frac{4x-4+4x+10}{(2x+5)(x-1)}$

$=\frac{8x+6}{(2x+5)(x-1)}$

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