Question
Perform each indicated operation.$$\left(\frac{a^{2}-b^{2}}{2 a^{2}-3 a b+b^{2}} \cdot \frac{2 a^{2}-7 a b+3 b^{2}}{a^{2}+a b}\right) \div \frac{a b-3 b^{2}}{a^{2}+2 a b+b^{2}}$$
Step 1
First, let's rewrite the division as multiplication by the reciprocal: $$ \left(\frac{a^{2}-b^{2}}{2 a^{2}-3 a b+b^{2}} \cdot \frac{2 a^{2}-7 a b+3 b^{2}}{a^{2}+a b}\right) \cdot \frac{a^{2}+2 a b+b^{2}}{a b-3 b^{2}} $$ Now, let's factor the expressions in the Show more…
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