$$\frac{a^{2}}{a+b}-a+b$$
$\frac{b^{2}}{a+b}$
$$\frac{a^{2}}{a+b}+\frac{\left(-a+b\right)\left(a+b\right)}{a+b}$$
$$\frac{a^{2}+\left(-a+b\right)\left(a+b\right)}{a+b}$$
$$\frac{a^{2}-a^{2}-ab+ba+b^{2}}{a+b}$$
$$\frac{b^{2}}{a+b}$$
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$-\left(\frac{b}{a+b}\right)^{2}$
