Question

In the following exercises, perform indicated operations.

$\frac{3}{r+4}+\frac{2}{r-5}$

Short answer

The resultant expression is$\frac{5r-7}{(r+4)(r-5)}$.

Step-by-step solution

Step 1. Given Information

The given expression is$\frac{3}{r+4}+\frac{2}{r-5}$.

Step 2. Express with common denominator  

• The LCD of the terms of given expression is $(r+4)(r-5)$.
• Multiply the numerator and denominator of first term by $(r-5)$and second term by $(r+4)$.

role="math" localid="1645165429857" $\frac{3(r-5)}{(r+4)(r-5)}+\frac{2(r+4)}{(r-5)(r+4)}=\frac{3r-15}{(r+4)(r-5)}+\frac{2r+8}{(r-5)(r+4)}$

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.

$\frac{3r-15+2r+8}{(r+4)(r-5)}=\frac{5r-7}{(r+4)(r-5)}$

• So, the resultant expression is $\frac{5r-7}{(r+4)(r-5)}$.