[tex]( \frac{x}{x+2} + \frac{4}{ x^{2} -3x-10} - \frac{2}{x-5} ): \frac{x-7}{ x^{2} +2x} [/tex]Упростите выражение. Created by chimkas. algebra-ru

tex]Упростите выражение...

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August 2021 1 39 Report

[tex]( \frac{x}{x+2} + \frac{4}{ x^{2} -3x-10} - \frac{2}{x-5} ): \frac{x-7}{ x^{2} +2x} [/tex]
Упростите выражение

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nelle987

Verified answer

$\left( \dfrac{x}{x+2} + \dfrac{4}{ x^{2} -3x-10} - \dfrac{2}{x-5} \right): \dfrac{x-7}{ x^{2} +2x} =\, ?\\
\dfrac x{x+2}+\dfrac4{x^2-3x-10}-\dfrac2{x-5}=\dfrac x{x+2}+\dfrac4{(x+2)(x-5)}-\dfrac2{x-5}=\\=
\dfrac{x(x-5)+4-2(x+2)}{(x+2)(x-5)}=\dfrac{x^2-7x}{(x+2)(x-5)}=\dfrac{x(x-7)}{(x+2)(x-5)}\\
\dfrac{x(x-7)}{(x+2)(x-5)}:\dfrac{x-7}{x^2+2x}=\dfrac{x(x-7)}{(x+2)(x-5)}\cdot\dfrac{x(x+2)}{x-7}=\dfrac{x^2}{x-5}$

$\boxed{\left( \dfrac{x}{x+2} + \dfrac{4}{ x^{2} -3x-10} - \dfrac{2}{x-5} \right): \dfrac{x-7}{ x^{2} +2x} =\dfrac{x^2}{x-5}}$

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