$$\frac{ { a }^{ 2 } +ab-2 { b }^{ 2 } }{ { a }^{ 2 } -2ab-3 { b }^{ 2 } } \times \frac{ { a }^{ 2 } - { b }^{ 2 } }{ ab+2 { b }^{ 2 } } \div \frac{ { a }^{ 2 } -2ab+ { b }^{ 2 } }{ { a }^{ 2 } -3ab }$$
Evaluate
$\frac{a}{b}$
Short Solution Steps
Multiply $\frac{a^{2}+ab-2b^{2}}{a^{2}-2ab-3b^{2}}$ times $\frac{a^{2}-b^{2}}{ab+2b^{2}}$ by multiplying numerator times numerator and denominator times denominator.
Divide $\frac{\left(a^{2}+ab-2b^{2}\right)\left(a^{2}-b^{2}\right)}{\left(a^{2}-2ab-3b^{2}\right)\left(ab+2b^{2}\right)}$ by $\frac{a^{2}-2ab+b^{2}}{a^{2}-3ab}$ by multiplying $\frac{\left(a^{2}+ab-2b^{2}\right)\left(a^{2}-b^{2}\right)}{\left(a^{2}-2ab-3b^{2}\right)\left(ab+2b^{2}\right)}$ by the reciprocal of $\frac{a^{2}-2ab+b^{2}}{a^{2}-3ab}$.
Multiply $\frac{a^{2}+ab-2b^{2}}{a^{2}-2ab-3b^{2}}$ times $\frac{a^{2}-b^{2}}{ab+2b^{2}}$ by multiplying numerator times numerator and denominator times denominator.
Divide $\frac{\left(a^{2}+ab-2b^{2}\right)\left(a^{2}-b^{2}\right)}{\left(a^{2}-2ab-3b^{2}\right)\left(ab+2b^{2}\right)}$ by $\frac{a^{2}-2ab+b^{2}}{a^{2}-3ab}$ by multiplying $\frac{\left(a^{2}+ab-2b^{2}\right)\left(a^{2}-b^{2}\right)}{\left(a^{2}-2ab-3b^{2}\right)\left(ab+2b^{2}\right)}$ by the reciprocal of $\frac{a^{2}-2ab+b^{2}}{a^{2}-3ab}$.
