$$\frac { a ^ { 2 } + a b - 2 b ^ { 2 } } { a ^ { 2 } - 2 a b - 3 b ^ { 2 } } \times \frac { a ^ { 2 } - b ^ { 2 } } { a b + 2 b ^ { 2 } } \div \frac { a ^ { 2 } - 2 a b + b ^ { 2 } } { a ^ { 2 } - 3 a b }$$
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 $\frac{a^{2}-2ab+b^{2}}{a^{2}-3ab}$.
