Question

Упростить выражения:
1. $x-y-frac{x^2+y^2}{x-y}$
2. $frac{a^2+b^2}{a+b}-a-b$

Answer 1

1) x -y -(x^2 +y^2)/(x-y) =
= [(x-y)^2 -x^2 -y^2]/(x-y) = (x^2 -2xy +y^2 -x^2 -y^2)/(x-y) = -2xy/(x-y) = 2xy/(y-x)

2) (a^2 +b^2)/(a+b) -a -b =
= [a^2 +b^2 -(a+b)^2]/(a+b) = (a^2 +b^2 -a^2 -2ab -b^2)/(a+b) = -2ab/(a+b)