Question

Сократите дробь (х^2-4ху+3у^2)/(х^2-5ху+4у^2)

Answer 1

$dfrac{x^2-4xy+3y^2}{x^2-5xy+4y^2}= dfrac{x^2-xy-3xy+3y^2}{x^2-xy-4xy+4y^2}= dfrac{x(x-y)-3y(x-y)}{x(x-y)-4y(x-y)}= \ \ = dfrac{(x-y)(x-3y)}{(x-y)(x-4y)}= dfrac{x-3y}{x-4y}$

Answer 2

$frac{ x^{2} -4xy+3 y^{2} }{ x^{2} -5xy+4 y^{2} } = frac{ x^{2} -4xy+4 y^{2} - y^{2} }{ x^{2} -xy-4xy+4 y^{2} } = frac{ (x-2y)^{2}- y^{2} }{x(x-y)-4y(x-y)} = frac{(x-y)*(x-3y)}{(x-4y)*(x-y)} = frac{x-3y}{x-4y}$