Question

In the following exercises, perform indicated operations.

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

Short answer

The resultant expression is$\frac{8x+6}{(2x+5)(x-1)}$.

Step-by-step solution

Step 1. Given Information

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

Step 2. Express with common denominator  

• The LCD of the terms of given expression is $(2x+5)(x-1)$.
• Multiply the numerator and denominator of first term by $(x-1)$and second term by $(2x+5)$.

role="math" localid="1645166494274" $\frac{4(x-1)}{(2x+5)(x-1)}+\frac{2(2x+5)}{(x-1)(2x+5)}=\frac{4x-4}{(2x+5)(x-1)}+\frac{4x+10}{(x-1)(2x+5)}$

Step 3. Simplify

• As the denominator is the same for both the terms, perform addition in the numerator and place it over the common denominator.

$\frac{4x-4+4x+10}{(2x+5)(x-1)}=\frac{8x+6}{(2x+5)(x-1)}$

• So, the resultant expression is $\frac{8x+6}{(2x+5)(x-1)}$.