Question

Efectuaţi:
$\frac{1}{x-y} + \frac{-y}{ x^{2} - y^{2}} =$

$\frac{\sqrt{2}x}{x-\sqrt{2}} + \frac{-2}{x-\sqrt{2}} =$

$\frac{1}{x(x-y)} - \frac{1}{y(x-y)} =$

$\frac{2x+1}{4x} - \frac{x^{2}-2}{4x^{2} -2x} =$

$\frac{1}{x(x+1)} - \frac{1}{(x+1)(x+2)} =$

Answer 1

a)  (x+y-y)/(x²-y²)=x/(x²-y²)
b)  (√2x-2)/(x-√2)
c)  (y-x)/xy(x-y)
d)  [(2x+1)(x-1)-2x²+4]/4x(x-1)=(2x²-x-1-2x²+4)/4x(x-1)=(3-x)/4x(x-1)
e)  (x+2-x)/x(x+1)(x+2)=2/x(x+1)(x+2)