Question

Упростите выражение (х^– 2 – у^– 2) : (х^– 1 + у^– 1)

Answer 1

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