Question

how do i simplify (y^-1+x^-1)/(xy)^-1

Answer 1

I'm assuming your equation is this:
\[\frac{y^{-1} + x^{-1}}{(xy)^{-1}}\]
Remember this rule of exponents:
\[a^{-b} = \frac{1}{a^b}\]
Applying that rule to this problem:
\[\frac{\frac{1}{y} + \frac{1}{x}}{\frac{1}{xy}}\]
Recall the use of reciprocals when dividing by fractions:
\[(\frac{1}{x} + \frac{1}{y}) * xy\]
Distribute the xy term:
\[\frac{xy}{x} + \frac{xy}{y}\]
Now we can cancel to get the answer:
\[y+x\]