Question

Упростите выражение.
(5/25-х^2 + 1/х-5) : х/2х^2-20х+50

Answer 1

$1)frac{5}{25-x^{2} } +frac{1}{x-5}=frac{5}{(5-x)(5+x)}-frac{1}{5-x}=frac{5-5-x}{(5-x)(5+x)}=-frac{x}{(5-x)(5+x)}=frac{x}{(x-5)(x+5)}\\2)frac{x}{(x-5)(x+5)}:frac{x}{2x^{2}-20x+50 }=frac{x}{(x-5)(x+5)}*frac{2(x^{2}-10x+25) }{x}= frac{2(x-5)^{2} }{(x-5)(x+5)}=frac{2x-10}{x+5}$