Question

Subtract$\frac{y^2-5y}{y^2-4}-\frac{6y-6}{4-y^2}$

Short answer

The required expression is$\frac{y+3}{y+2}$.

Step-by-step solution

Given information

The given expression is$\frac{y^2-5y}{y^2-4}-\frac{6y-6}{4-y^2}$

Simplifying the expression

The denominators of the two rational expressions are opposite so multiply the second rational expression with $\frac{-1}{-1}:$

$\frac{y^2-5y}{y^2-4}-\frac{(-1)(6y-6)}{(-1)(4-y^2)}$

Simplifying the second expression:

$\frac{y^2-5y}{y^2-4}+\frac{6y-6}{y^2-4}$

Combining the expressions:

$\frac{y^2-5y+6y-6}{y^2-4}$

Combining the like terms:

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

Factorizing the numerator and denominator:

$\frac{(y+3)(y-2)}{(y-2)(y+2)}$

Cancel the common terms in numerator and denominator:

$\frac{y+3}{y+2}.$