Question

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Answer 1

$\left(a^{2}-b^{2} \right )+\left(\dfrac{a^{2}+ab}{b^{2}+ab}+\dfrac{a^{2}-ab}{b^{2}-ab} \right )\\ \\ =\left(a^{2}-b^{2} \right )+\left(\dfrac{a\cdot\left(a+b \right )}{b\cdot\left(b+a \right )}+\dfrac{a\cdot\left(a-b \right )}{-b \cdot \left(-b+a\right)} \right )\\ \\ =\left(a^{2}-b^{2} \right )+\left(\dfrac{a\cdot\left(a+b \right )}{b\cdot\left(a+b \right )}+\dfrac{a\cdot\left(a-b \right )}{-b \cdot \left(a-b\right)} \right )\\ \\ =\left(a^{2}-b^{2} \right )+\left(\dfrac{a}{b}+\dfrac{a}{-b } \right )\\ \\ =\left(a^{2}-b^{2} \right )+\left(\dfrac{a}{b}-\dfrac{a}{b} \right )\\ \\ =\left(a^{2}-b^{2} \right )+0\\ \\ =a^{2}-b^{2}$