Use Square of Sum: \({(a+b)}^{2}={a}^{2}+2ab+{b}^{2}\).
\[\frac{\frac{{x}^{2}}{x+y}-\frac{{x}^{3}}{{(x+y)}^{2}}}{\frac{x}{x+y}-\frac{{x}^{2}}{{}^{2-{y}^{2}}}}\]
Factor out the common term \({x}^{2}\).
\[\frac{{x}^{2}(\frac{1}{x+y}-\frac{x}{{(x+y)}^{2}})}{\frac{x}{x+y}-\frac{{x}^{2}}{{}^{2-{y}^{2}}}}\]
Rewrite the expression with a common denominator.
\[\frac{{x}^{2}\times \frac{x+y-x}{{(x+y)}^{2}}}{\frac{x}{x+y}-\frac{{x}^{2}}{{}^{2-{y}^{2}}}}\]
Collect like terms.
\[\frac{{x}^{2}\times \frac{(x-x)+y}{{(x+y)}^{2}}}{\frac{x}{x+y}-\frac{{x}^{2}}{{}^{2-{y}^{2}}}}\]
Simplify \((x-x)+y\) to \(y\).
\[\frac{{x}^{2}\times \frac{y}{{(x+y)}^{2}}}{\frac{x}{x+y}-\frac{{x}^{2}}{{}^{2-{y}^{2}}}}\]
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\frac{\frac{{x}^{2}y}{{(x+y)}^{2}}}{\frac{x}{x+y}-\frac{{x}^{2}}{{}^{2-{y}^{2}}}}\]
Use this rule: \(\frac{a}{b} \times c=\frac{ac}{b}\).
\[\frac{\frac{{x}^{2}y}{{(x+y)}^{2}}}{\frac{x}{x+y}-{x}^{2}{}^{2-{y}^{2}}}\]
Factor out the common term \(x\).
\[\frac{\frac{{x}^{2}y}{{(x+y)}^{2}}}{x(\frac{1}{x+y}-x{}^{2-{y}^{2}})}\]
Simplify.
\[\frac{{x}^{2}y}{x{(x+y)}^{2}(\frac{1}{x+y}-x{}^{2-{y}^{2}})}\]
Simplify.
\[\frac{xy}{{(x+y)}^{2}(\frac{1}{x+y}-x{}^{2-{y}^{2}})}\]
(x*y)/((x+y)^2*(1/(x+y)-x*^(2-y^2)))
