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\frac{\frac{y}{xy}+\frac{x}{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 and y is xy. Multiply \frac{1}{x} times \frac{y}{y}. Multiply \frac{1}{y} times \frac{x}{x}.
\frac{\frac{y+x}{xy}}{\frac{1}{x^{2}}-\frac{1}{y^{2}}}
Since \frac{y}{xy} and \frac{x}{xy} have the same denominator, add them by adding their numerators.
\frac{\frac{y+x}{xy}}{\frac{y^{2}}{x^{2}y^{2}}-\frac{x^{2}}{x^{2}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{y+x}{xy}}{\frac{y^{2}-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{\left(y+x\right)x^{2}y^{2}}{xy\left(y^{2}-x^{2}\right)}
Divide \frac{y+x}{xy} by \frac{y^{2}-x^{2}}{x^{2}y^{2}} by multiplying \frac{y+x}{xy} by the reciprocal of \frac{y^{2}-x^{2}}{x^{2}y^{2}}.
\frac{xy\left(x+y\right)}{-x^{2}+y^{2}}
Cancel out xy in both numerator and denominator.
\frac{xy\left(x+y\right)}{\left(x+y\right)\left(-x+y\right)}
Factor the expressions that are not already factored.
\frac{xy}{-x+y}
Cancel out x+y in both numerator and denominator.
\frac{\frac{y}{xy}+\frac{x}{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 and y is xy. Multiply \frac{1}{x} times \frac{y}{y}. Multiply \frac{1}{y} times \frac{x}{x}.
\frac{\frac{y+x}{xy}}{\frac{1}{x^{2}}-\frac{1}{y^{2}}}
Since \frac{y}{xy} and \frac{x}{xy} have the same denominator, add them by adding their numerators.
\frac{\frac{y+x}{xy}}{\frac{y^{2}}{x^{2}y^{2}}-\frac{x^{2}}{x^{2}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{y+x}{xy}}{\frac{y^{2}-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{\left(y+x\right)x^{2}y^{2}}{xy\left(y^{2}-x^{2}\right)}
Divide \frac{y+x}{xy} by \frac{y^{2}-x^{2}}{x^{2}y^{2}} by multiplying \frac{y+x}{xy} by the reciprocal of \frac{y^{2}-x^{2}}{x^{2}y^{2}}.
\frac{xy\left(x+y\right)}{-x^{2}+y^{2}}
Cancel out xy in both numerator and denominator.
\frac{xy\left(x+y\right)}{\left(x+y\right)\left(-x+y\right)}
Factor the expressions that are not already factored.
\frac{xy}{-x+y}
Cancel out x+y in both numerator and denominator.