Question

Simplify

(x^-1 y^-1)/(x^-1 + y^-1)

Answer 1

ANSWER:

To Simplify:

• (x^-1 y^-1)/(x^-1 + y^-1)

Solution:

We are given that,

$\implies\rm{\dfrac{x^{-1}y^{-1}}{x^{-1}+y^{-1}}}$

We know that,

$\hookrightarrow\rm{a^m\times b^m=(a\times b)^m}$

So,

$\implies\rm{\dfrac{x^{-1}y^{-1}}{x^{-1}+y^{-1}}}$

$\implies\rm{\dfrac{(xy)^{-1}}{x^{-1}+y^{-1}}}$

We know that,

$\hookrightarrow\rm{a^{-1}=\dfrac{1}{a}}$

So,

$\implies\rm{\dfrac{(xy)^{-1}}{x^{-1}+y^{-1}}}$

$\implies\rm{\dfrac{\dfrac{1}{xy}}{\dfrac{1}{x}+\dfrac{1}{y}}}$

Taking LCM in denominator,

$\implies\rm{\dfrac{\dfrac{1}{xy}}{\dfrac{1}{x}+\dfrac{1}{y}}}$

$\implies\rm{\dfrac{\dfrac{1}{xy}}{\dfrac{x+y}{xy}}}$

Cancelling xy,

$\implies\rm{\dfrac{1}{x+y}}$

So,

$\implies\bf{(x+y)^{-1}}$