Прошу сократить 1) [latex] \frac{3x-y}{x-2y} [/latex] * [latex] \frac{2x+4y}{9x^2+6xy+y^2} [/latex] 2) [latex] \frac{x^2-y^2}{27x^3} [/latex] * [latex] \frac{18x^2}{xy-y^2} [/latex]3) [latex] \frac{a-20}{a-8} [/latex] / [latex...

Question

Прошу сократить 1) [latex] \frac{3x-y}{x-2y} [/latex] * [latex] \frac{2x+4y}{9x^2+6xy+y^2} [/latex] 2) [latex] \frac{x^2-y^2}{27x^3} [/latex] * [latex] \frac{18x^2}{xy-y^2} [/latex]3) [latex] \frac{a-20}{a-8} [/latex] / [latex...

Прошу сократить 1) [latex] \frac{3x-y}{x-2y} [/latex] * [latex] \frac{2x+4y}{9x^2+6xy+y^2} [/latex] 2) [latex] \frac{x^2-y^2}{27x^3} [/latex] * [latex] \frac{18x^2}{xy-y^2} [/latex] 3) [latex] \frac{a-20}{a-8} [/latex] / [latex] \frac{a^2-400}{a^2-16a+64} [/latex] 4) [latex] \frac{xy}{xy+3y^2} [/latex] / [latex] \frac{x^2}{x^2+6xy+9y^2} [/latex]

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Ответ(ы) на вопрос:

Accepted Answer

[latex]1)...=\frac{3x-y}{x-2y}\cdot \frac{2(x+2y)}{(3x+y)^2}\\2)...=\frac{(x-y)(x+y)\cdot 18x^2}{27x^3\cdot y(x-y)}=\frac{2(x+y)}{3xy}\\3) ...=\frac{(a-20)(a-8)^2}{(a-8)(a-20)(a+20)}=\frac{a-8}{a+20}\\4)...=\frac{xy\cdot (x+3y)^2}{y(x+3y)\cdot x^2}=\frac{x+3y}{x}[/latex]