Question

Which expression is equal to ${(x^{-1}+y^{-1})}^{-1}$?

• A. $xy$
• B. $x+y$
• C. $\frac{xy}{(x+y)}$
• D. $\frac{(x+y)}{xy}$

Answer 1

The correct option is C

$\frac{xy}{(x+y)}$

The explanation for correct answers:

Simpifying the expression:

Determine the expression ${(x^{-1}+y^{-1})}^{-1}$.

$\begin{array}{rcl}{(x^{-1}+y^{-1})}^{-1}& =& {(\frac{1}{x}+\frac{1}{y})}^{-1}\\ & =& \frac{1}{(\frac{1}{x}+\frac{1}{y})}\\ & =& \frac{1}{\left(\frac{y+x}{xy}\right)}\\ & =& \frac{xy}{x+y}\end{array}$

Hence, ${(x^{-1}+y^{-1})}^{-1}$expression is equal to $“\frac{xy}{x+y}”$..

Hence ‘option C’ is the correct answer.