Question

$( frac{x}{x+2} + frac{4}{ x^{2} -3x-10} - frac{2}{x-5} ): frac{x-7}{ x^{2} +2x}$
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Answer 1

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

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