Сократите дробь (х^2-4ху+3у^2)/(х^2-5ху+4у^2). Created by Natalii2017. algebra-ru

(х^2-5ху+4у^2)...

Natalii2017 @Natalii2017

August 2021 2 2 Report

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

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

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

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