Question

In the following exercises, subtract.

$\frac{5r^2+7r-33}{r^2-49}-\frac{4r^2+5r+30}{r^2-49}$

Short answer

The resultant expression is$\frac{r+9}{r+7}$.

Step-by-step solution

Step 1. Given Information

The given expression is$\frac{5r^2+7r-33}{r^2-49}-\frac{4r^2+5r+30}{r^2-49}$.

Step 2. Subtract the numerator

As the denominator is the same for both the terms, subtract the numerator and place it over the common denominator.

$\begin{array}{rcl}\frac{5r^2+7r-33}{r^2-49}-\frac{4r^2+5r+30}{r^2-49}& =& \frac{5r^2+7r-33-4r^2-5r-30}{r^2-49}\\ & =& \frac{r^2+2r-63}{r^2-49}\end{array}$

Step 3. Factor the expression   

• Factor the expression in the numerator and denominator, and then cancel out the common terms from the numerator and denominator.

$\frac{(r-7)(r+9)}{(r-7)(r+7)}=\frac{r+9}{r+7}$

• So, the resultant expression is $\frac{r+9}{r+7}$.