Question

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

Answer 1

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