Question

Simplify: $\frac{3y(x-y)-2x(y-2x)}{7x(x-y)-3\left(x^2{-y}^2\right)}$

• A. $\frac{x-y}{x+y}$
• B. $1$
• C. $\frac{x+y}{x-y}$
• D. $0$

Answer 1

The correct option is C $\frac{x+y}{x-y}$

Given $\frac{3y(x-y)-2x(y-2x)}{7x(x-y)-3\left(x^2{-y}^2\right)}$
$=\frac{3xy-3y^2-2xy+4x^2}{7x^2-7xy-3x^2+3y^2}$
$=\frac{4x^2+xy+3y^2}{4x^2-7xy+3y^2}$
$=\frac{4x^2+4xy-3xy-3y^2}{4x^2-4xy-3xy+3y^2}$
$=\frac{4x(x+y)-3y(x+y)}{4x(x-y)-3y(x-y)}$
$=\frac{(4x-3y)(x+y)}{(4x-3y)(x-y)}$
$=\frac{x+y}{x-y}$