Question

упростить выражение

Answer 1

$1)frac{x^{2}-y^{2}  }{3x-3y } =frac{(x-y)*(x+y)}{3(x-y)}=frac{x+y}{3};\   2) (frac{5y}{y}-frac{x}{5y}):frac{x}{y} =(5-frac{x}{5y})*frac{y}{x}=frac{25y-x}{5y}*frac{y}{x}=frac{25y-x}{5}*frac{1}{x}=frac{25y-x}{5x}$

$3)(4x-frac{12x}{x-2}) : (x-frac{8x-25}{x-2})=frac{4x*(x-2)-12x}{x-2}:frac{x*(x-2)-(8x-25)}{x-2}=frac{4x^{2}-8x-12x }{x-2} :frac{x^{2}-2x-8x+25 }{x-2}=frac{4x^2-20x}{x-2}*frac{x^2-10x+25}{x-2}=frac{4x*(x-5)}{x-2} *frac{x-2}{x^2-10x+25}=4x*(x-5)*frac{1}{(x-5)^{2} } =4x*frac{1}{x-5}=frac{4x}{x-5}$