Question

In the following exercises, subtract.

$\frac{7t^2-t-4}{t^2-25}-\frac{6t^2+12t-44}{t^2-25}$

Short answer

The resultant expression is$\frac{t-8}{t+5}$.

Step-by-step solution

Step 1. Given Information

The given expression is$\frac{7t^2-t-4}{t^2-25}-\frac{6t^2+12t-44}{t^2-25}$.

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.

$\begin{array}{rcl}\frac{7t^2-t-4}{t^2-25}-\frac{6t^2+12t-44}{t^2-25}& =& \frac{7t^2-t-4-6t^2-12t+44}{t^2-25}\\ & =& \frac{t^2-13t+40}{t^2-25}\end{array}$

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.

$\frac{(t-5)(t-8)}{(t-5)(t+5)}=\frac{t-8}{t+5}$

• So, the resultant expression is $\frac{t-8}{t+5}$.