Question

Subtract$\frac{6x^2-x+20}{x^2-81}-\frac{5x^2+11x-7}{x^2-81}$

Short answer

The required expression is$\frac{x-3}{x+9}$.

Step-by-step solution

Given information

The given expression is$\frac{6x^2-x+20}{x^2-81}-\frac{5x^2+11x-7}{x^2-81}$

Simplifying the expression

Making the denominator same:

$\frac{6x^2-x+20-(5x^2+11x-7)}{x^2-81}$

Combine like terms:

$\frac{x^2-12x+27}{x^2-81}$

Factor the numerator and denominator:

$\frac{(x-9)(x-3)}{(x-9)(x+9)}$

Cancel the common terms from numerator and denominator:

$\frac{(x-3)}{(x+9)}.$