Simplify (x^-2+y^-2)/((xy)^-1)

$\frac{x^{- 2} + y^{- 2}}{{(x y)}^{- 1}}$

Move ${(x y)}^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$(x^{- 2} + y^{- 2}) (x y)$

Simplify each term.

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$(\frac{1}{x^{2}} + y^{- 2}) (x y)$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$(\frac{1}{x^{2}} + \frac{1}{y^{2}}) (x y)$

To write $\frac{1}{x^{2}}$ as a fraction with a common denominator, multiply by $\frac{y^{2}}{y^{2}}$ .

$(\frac{1}{x^{2}} \cdot \frac{y^{2}}{y^{2}} + \frac{1}{y^{2}}) (x y)$

To write $\frac{1}{y^{2}}$ as a fraction with a common denominator, multiply by $\frac{x^{2}}{x^{2}}$ .

$(\frac{1}{x^{2}} \cdot \frac{y^{2}}{y^{2}} + \frac{1}{y^{2}} \cdot \frac{x^{2}}{x^{2}}) (x y)$

Write each expression with a common denominator of $x^{2} y^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{x^{2}}$ by $\frac{y^{2}}{y^{2}}$ .

$(\frac{y^{2}}{x^{2} y^{2}} + \frac{1}{y^{2}} \cdot \frac{x^{2}}{x^{2}}) (x y)$

Multiply $\frac{1}{y^{2}}$ by $\frac{x^{2}}{x^{2}}$ .

$(\frac{y^{2}}{x^{2} y^{2}} + \frac{x^{2}}{y^{2} x^{2}}) (x y)$

Reorder the factors of $y^{2} x^{2}$ .

$(\frac{y^{2}}{x^{2} y^{2}} + \frac{x^{2}}{x^{2} y^{2}}) (x y)$

Combine the numerators over the common denominator.

$\frac{y^{2} + x^{2}}{x^{2} y^{2}} (x y)$

Cancel the common factor of $x y$ .

Factor $x y$ out of $x^{2} y^{2}$ .

$\frac{y^{2} + x^{2}}{x y (x y)} (x y)$

Cancel the common factor.

$\frac{y^{2} + x^{2}}{x y (x y)} (x y)$

Rewrite the expression.

$\frac{y^{2} + x^{2}}{x y}$