Question

$simplificando \: ({x }^{ - 1} + {y}^{ - 1} ) ^{ - 1} \times ({xy})^{ - 1} obtem -se \: \\ a) \: x + y \\ b) \: x - y \\ c) \: (x + y)^{ - 1} \\ d) \: 2x - y \\ e) \: 1$

Answer 1

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