Question

Add and Subtract Rational Expressions whose Denominators are Opposites

In the following exercises, add and subtract.

$\frac{2b^2+3b-15}{b^2-49}-\frac{b^2+16b-1}{49-b^2}.$

Short answer

The answer is$\frac{3b^2+19b-16}{b^2-49}.$

Step-by-step solution

Step 1. Given Information.

Given:

$\frac{2b^2+3b-15}{b^2-49}-\frac{b^2+16b-1}{49-b^2}$ having the same denominator just with opposite sign.

Step 2. Creating the denominator exactly same.

Now take a minus sign out of denominator of second term in the above expression we get:

$\frac{2b^2+3b-15}{b^2-49}+\frac{b^2+16b-1}{b^2-49}.$

Now we can clearly see that the denominators are same.

Step 3. Solving the expression in step 2. 

Now as the denominators are same so we can directly subtract the numerators:

$$\begin{gathered} \frac{2b^2+3b-15}{b^2-49}+\frac{b^2+16b-1}{b^2-49} \\ =\frac{2b^2+3b-15+b^2+16b-1}{b^2-49} \\ =\frac{3b^2+19b-16}{b^2-49}. \\ Since,theabovequadraticexpressionisnotfactorizablesothisisouranswer. \end{gathered}$$