Question

Упростить выражение. 

Answer 1

решим по действиям:
1) y/(xy-x²)+x/(xy-y²)=y/(x(y-x)+x/(y(x-y)=y/(x(y-x)-x/(y(y-x)=(y²-x²)/(xy(y-x))=((y-x)(y+x))/(xy(y-x))=(y+x)/(xy)
2)1/x+1/y=(x+y)/xy
3) x²+2xy+y²=(x+y)²
4)(x+y)²:((x+y)/xy)=(x+y)²*(xy/(x+y))=xy(x+y)
5)(y+x)/(xy):xy(x+y)=1/(x²y²)

Answer 2

$( frac{y}{xy-x^2}+ frac{x}{xy-y^2}): frac{x^2-2xy+y^2}{ frac{1}{x}+ frac{1}{y} }= \ =( frac{y}{x(y-x)}- frac{x}{y(y-x}): frac{(x+y)^2}{ frac{y+x}{xy}}= \ =frac{y^2-x^2}{xy(y-x)}* frac{x+y}{xy(x+y)^2} = \ = =frac{(y-x)(y+x)}{xy(y-x)}* frac{x+y}{xy(x+y)^2}= frac{1}{x^2y^2}$