Question

In the following exercises, perform indicated operations.

Short answer

The resultant expression is$\frac{-6}{m+6}$.

Step-by-step solution

Step 1. Given Information 

The given expression is$\frac{6}{m+6}-\frac{12m}{m^2-36}$.

Step 2. Express with LCD

• The LCD of the given expressions to subtract is $(m-6)(m+6)$.
• Express the given expression with LCD.

$\frac{6}{m+6}-\frac{12m}{m^2-36}=\frac{6m-36}{\left(m+6\right)\left(m-6\right)}-\frac{12m}{\left(m+6\right)\left(m-6\right)}$

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.

$\begin{array}{rcl}\frac{6m-36}{\left(m+6\right)\left(m-6\right)}-\frac{12m}{\left(m+6\right)\left(m-6\right)}& =& \frac{6m-36-12m}{\left(m+6\right)\left(m-6\right)}\\ & =& \frac{-6m-36}{\left(m+6\right)\left(m-6\right)}\end{array}$

• Cancel out the common factor from numerator and denominator.

$\begin{array}{rcl}\frac{-6m-36}{\left(m+6\right)\left(m-6\right)}& =& \frac{-6\cancel{\left(m+6\right)}}{\cancel{\left(m+6\right)}\left(m-6\right)}\\ & =& \frac{-6}{m+6}\end{array}$

• So, the resultant expression is$\frac{-6}{m+6}$.