Question

Simplify $(x^{-1}+y^{-1})$.

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

Answer 1

The correct option is C $\frac{x+y}{xy}$


We know that $a^{-n}=\frac{1}{n}$
$\therefore x^{-1}=\frac{1}{x}$ and $y^{-1}=\frac{1}{y}$
$\Rightarrow$ $x^{-1}+y^{-1}=\frac{1}{x}+\frac{1}{y}=\frac{y+x}{xy}=\frac{x+y}{xy}$