Solve x^-2-y^-2/x^-1y^-1

$$\frac { x ^ { - 2 } - y ^ { - 2 } } { x ^ { - 1 } y ^ { - 1 } }$$

Evaluate

$$\frac{y^{2}-x^{2}}{xy}$$

Short Solution Steps

Factor the expressions that are not already factored.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

Expand the expression.

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

Express \frac{1}{y}x as a single fraction.

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

To raise \frac{x}{y} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1-\frac{x^{2}}{y^{2}}}{\frac{1}{y}x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{y^{2}}{y^{2}}.

$$\frac{\frac{y^{2}}{y^{2}}-\frac{x^{2}}{y^{2}}}{\frac{1}{y}x}$$

Since \frac{y^{2}}{y^{2}} and \frac{x^{2}}{y^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{y^{2}-x^{2}}{y^{2}}}{\frac{1}{y}x}$$

Express \frac{1}{y}x as a single fraction.

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

Divide \frac{y^{2}-x^{2}}{y^{2}} by \frac{x}{y} by multiplying \frac{y^{2}-x^{2}}{y^{2}} by the reciprocal of \frac{x}{y}.

$$\frac{\left(y^{2}-x^{2}\right)y}{y^{2}x}$$

Cancel out y in both numerator and denominator.

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

Expand

$$\frac{y^{2}-x^{2}}{xy}$$

Short Solution Steps

Factor the expressions that are not already factored.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

Expand the expression.

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

Express \frac{1}{y}x as a single fraction.

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

To raise \frac{x}{y} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1-\frac{x^{2}}{y^{2}}}{\frac{1}{y}x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{y^{2}}{y^{2}}.

$$\frac{\frac{y^{2}}{y^{2}}-\frac{x^{2}}{y^{2}}}{\frac{1}{y}x}$$

Since \frac{y^{2}}{y^{2}} and \frac{x^{2}}{y^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{y^{2}-x^{2}}{y^{2}}}{\frac{1}{y}x}$$

Express \frac{1}{y}x as a single fraction.

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

Divide \frac{y^{2}-x^{2}}{y^{2}} by \frac{x}{y} by multiplying \frac{y^{2}-x^{2}}{y^{2}} by the reciprocal of \frac{x}{y}.

$$\frac{\left(y^{2}-x^{2}\right)y}{y^{2}x}$$

Cancel out y in both numerator and denominator.

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