Question

Add and Subtract Rational Expressions with a Common Denominator

In the following exercises, perform the indicated operations.

Answer 1

`\displaystyle (4q^2-q+3)/(q^2+6q+5)-(3q^2-q-6)/(q^2+6q+5)=(q^2+9)/(q^2+6q+5)`

Explanation:

Simplifying Rational Expressions

If two or more rational expressions have the same denominator, the add and subtract operations are done only with the numerator. The final denominator will be the common of both.

The expression is:

`\displaystyle (4q^2-q+3)/(q^2+6q+5)-(3q^2-q-6)/(q^2+6q+5)`

Operating on the numerators:

`\displaystyle (4q^2-q+3)/(q^2+6q+5)-(3q^2-q-6)/(q^2+6q+5)=(4q^2-q+3-(3q^2-q-6))/(q^2+6q+5)`

Removing parentheses:

`\displaystyle (4q^2-q+3)/(q^2+6q+5)-(3q^2-q-6)/(q^2+6q+5)=(4q^2-q+3-3q^2+q+6)/(q^2+6q+5)`

Simplifying:

`\boxed{\displaystyle (4q^2-q+3)/(q^2+6q+5)-(3q^2-q-6)/(q^2+6q+5)=(q^2+9)/(q^2+6q+5)}`

The expression cannot be further simplified.