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