Question

спростiть вираз (x/x^2-25 - x-8/x^2-10x+25) : x-20/(x-5)^2

Answer 1

$(frac{x}{x^{2} -25}-frac{x-8}{x^{2}-10x+25 }):frac{x-20}{(x-5)^{2} }=(frac{x}{(x-5)(x+5)}-frac{x-8}{(x-5)^{2} }):frac{x-20}{(x-5)^{2} }=frac{x^{2}-5x-x^{2}+8x-5x+40}{(x-5)^{2}(x+5) }:frac{x-20}{(x-5)^{2} }=frac{40-2x}{(x-5)^{2}(x+5)}*frac{(x-5)^{2} }{x-20}=frac{2(20-x)}{(x+5)(x-20)}=-frac{2}{x+5}$