Question

Add$\frac{6y^2+7y-10}{4y-7}+\frac{2y^2+2y+11}{7-4y}$.

Short answer

The required expression is$y+3.$

Step-by-step solution

Given information

The given expression is

$\frac{6y^2+7y-10}{4y-7}+\frac{2y^2+2y+11}{7-4y}$

Simplifying the expression

The denominators of the two expressions are opposite to each other, so multiply the second rational expression with $\frac{6y^2+7y-10}{4y-7}+\frac{(-1)(2y^2+2y+11)}{(-1)(7-4y)}$

Simplifying the second expression:

$\frac{6y^2+7y-10}{4y-7}+\frac{-2y^2-2y-11}{4y-7}$

Combine like terms:

Factor the numerator:

$\frac{(4y-7)(y+3)}{4y-7}$

Cancel the like factors from numerator and denominator:

$y+3.$