Question

Simplifique a expressão (1/y - 1/x) . (x² + xy/x² - y²)

Lembrando que "." É vezes (x)

Answer 1

$Resolu\c{c}\~ao \to \left\{\begin{array}{ccc}(\frac{1}{y}-\frac{1}{x})*(\frac{x^2+xy}{x^2-y^2})=\\\\(\frac{x-y}{xy})*(\frac{x*(x+y)}{(x+y)*(x-y)})=\\\\\frac{(x-y)}{xy}*\frac{x}{(x-y)} = \\\\\frac{x}{xy} = \\\\\boxed{\boxed{\frac{1}{y}}}\end{array}\right$

Espero ter ajudado. =^.^=

Answer 2

Oie, Td Bom?!

>>> Resolvendo a expressão.

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

$\frac{x - y}{xy} \: . \: \frac{x {}^{2} + xy }{x {}^{2} - y {}^{2} }$

$\frac{x - y}{xy} \: . \: \frac{x \: . \: (x + y)}{x {}^{2} - y {}^{2} }$

$\frac{x - y}{xy} \: . \: \frac{x \: . \: (x + y)}{(x - y) \: . \: ( x + y)}$

$\frac{x - y}{xy} \: . \: \frac{x}{x - y}$

$\frac{1}{xy} \: . \: x$

$\frac{1}{y}$

Att. Makaveli1996