Question

Subtract$\frac{4x^2-11x+8}{x^2-3x+2}-\frac{3x^2+x-3}{x^2-3x+2}$

Short answer

The required expression is$\frac{x-11}{x-2}$

Step-by-step solution

Given information

The given expression is$\frac{4x^2-11x+8}{x^2-3x+2}-\frac{3x^2+x-3}{x^2-3x+2}$

Simplifying the expression

Making the denominator same:

$\frac{4x^2-11x+8-(3x^2+x-3)}{x^2-3x+2}$

Distribute the negative sign:

$\frac{4x^2-11x+8-3x^2-x+3}{x^2-3x+2}$

Combine like terms:

$\frac{x^2-12x+11}{x^2-3x+2}$

Factor numerator and denominator:

role="math" $\frac{(x-11)(x-1)}{(x-1)(x-2)}$

Cancel the common term from the numerator and denominator:

$\frac{(x-11)}{(x-2)}$