Question

In the following exercises, perform indicated operations.

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

Short answer

The resultant expression is$\frac{3z^2+16z-2}{(z-2)(z+5)}$.

Step-by-step solution

Step 1. Given Information

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

Step 2. Express with common denominator    

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

role="math" localid="1645170888912" $\frac{3z(z+5)}{(z-2)(z+5)}+\frac{1(z-2)}{(z+5)(z-2)}=\frac{3z^2+15z}{(z-2)(z+5)}+\frac{z-2}{(z+5)(z-2)}$

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.

$\frac{3z^2+15z+z-2}{(z-2)(z+5)}=\frac{3z^2+16z-2}{(z-2)(z+5)}$

• So, the resultant expression is $\frac{3z^2+16z-2}{(z-2)(z+5)}$.