Solve x/y-y/x/frac{1{x^2}-1/y^2}=

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

Evaluate

$$-xy$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x is xy. Multiply \frac{x}{y} times \frac{x}{x}. Multiply \frac{y}{x} times \frac{y}{y}.

$$\frac{\frac{xx}{xy}-\frac{yy}{xy}}{\frac{1}{x^{2}}-\frac{1}{y^{2}}}$$

Since \frac{xx}{xy} and \frac{yy}{xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{xx-yy}{xy}}{\frac{1}{x^{2}}-\frac{1}{y^{2}}}$$

Do the multiplications in xx-yy.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2} and y^{2} is x^{2}y^{2}. Multiply \frac{1}{x^{2}} times \frac{y^{2}}{y^{2}}. Multiply \frac{1}{y^{2}} times \frac{x^{2}}{x^{2}}.

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

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

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

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

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

Extract the negative sign in x^{2}-y^{2}.

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

Cancel out xy\left(-x^{2}+y^{2}\right) in both numerator and denominator.

$$-xy$$

Expand

$$-xy$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x is xy. Multiply \frac{x}{y} times \frac{x}{x}. Multiply \frac{y}{x} times \frac{y}{y}.

$$\frac{\frac{xx}{xy}-\frac{yy}{xy}}{\frac{1}{x^{2}}-\frac{1}{y^{2}}}$$

Since \frac{xx}{xy} and \frac{yy}{xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{xx-yy}{xy}}{\frac{1}{x^{2}}-\frac{1}{y^{2}}}$$

Do the multiplications in xx-yy.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2} and y^{2} is x^{2}y^{2}. Multiply \frac{1}{x^{2}} times \frac{y^{2}}{y^{2}}. Multiply \frac{1}{y^{2}} times \frac{x^{2}}{x^{2}}.

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

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

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

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

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

Extract the negative sign in x^{2}-y^{2}.

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

Cancel out xy\left(-x^{2}+y^{2}\right) in both numerator and denominator.

$$-xy$$