Question

In the following exercises, perform indicated operations.

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

Short answer

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

Step-by-step solution

Step 1. Given Information

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

Step 2. Express with common denominator 

• The LCD of the terms of given expression is $(3w-2)(w+1)$.
• Multiply the numerator and denominator of first term by $(w+1)$and second term by $(3w-2)$.

role="math" localid="1645166143677" $\frac{5(w+1)}{(3w-2)(w+1)}+\frac{2(3w-2)}{(w+1)(3w-2)}=\frac{5w+5}{(3w-2)(w+1)}+\frac{6w-4}{(w+1)(3w-2)}$

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.

$\frac{5w+5+6w-4}{(3w-2)(w+1)}=\frac{11w+1}{(3w-2)(w+1)}$

• So, the resultant expression is $\frac{11w+1}{(3w-2)(w+1)}$.