Question

Simplify the following two polynomials in the simplest form: $\frac{2x^2-5x+3}{x^2-3x+2}-\frac{2x^2-7x-4}{2x^2-3x-2}$

• A. $\frac{x+1}{x-2}$
• B. $\frac{x-1}{x-2}$
• C. $\frac{x+1}{x+2}$
• D. None of these

Answer 1

The correct option is A $\frac{x+1}{x-2}$

The given expression $\frac{2x^2-5x+3}{x^2-3x+2}-\frac{2x^2-7x-4}{2x^2-3x-2}$can be simplified as shown below:

$=\frac{2x^2-5x+3}{x^2-3x+2}-\frac{2x^2-7x-4}{2x^2-3x-2}$

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

$=\frac{2x(x-1)-3(x-1)}{x(x-1)-2(x-1)}-\frac{2x(x-4)+1(x-4)}{2x(x-2)+1(x-2)}$

$=\frac{(2x-3)(x-1)}{(x-2)(x-1)}-\frac{(2x+1)(x-4)}{(2x+1)(x-2)}$

$=\frac{2x-3}{x-2}-\frac{x-4}{x-2}$

$=\frac{(2x-3)-(x-4)}{x-2}$

$=\frac{2x-3-x+4}{x-2}$

$=\frac{x+1}{x-2}$

Hence, $\frac{2x^2-5x+3}{x^2-3x+2}-\frac{2x^2-7x-4}{2x^2-3x-2}=\frac{x+1}{x-2}$.