Question
Perform the indicated operations and, if possible, simplify.$$\frac{a^{3}-a b^{2}}{2 a^{2}+3 a b+b^{2}} \cdot \frac{4 a^{2}-b^{2}}{a^{2}-2 a b+b^{2}} \div \frac{a^{2}+a}{a-1}$$
Step 1
We can factorize the numerator and denominator of each fraction as follows: $$ \frac{a^{3}-a b^{2}}{2 a^{2}+3 a b+b^{2}} = \frac{a(a^{2}-b^{2})}{(2a+b)(a+b)} $$ $$ \frac{4 a^{2}-b^{2}}{a^{2}-2 a b+b^{2}} = \frac{(2a-b)(2a+b)}{(a-b)^{2}} $$ $$ \frac{a^{2}+a}{a-1} = Show more…
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