Solve 3a^2+a-2/4a^2+7a+3/frac{3a^2-8a+4{4a^2-5a-6}}

$$\frac{ \frac{ 3 { a }^{ 2 } +a-2 }{ 4 { a }^{ 2 } +7a+3 } }{ \frac{ 3 { a }^{ 2 } -8a+4 }{ 4 { a }^{ 2 } -5a-6 } }$$

Evaluate

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Short Solution Steps

Divide \frac{3a^{2}+a-2}{4a^{2}+7a+3} by \frac{3a^{2}-8a+4}{4a^{2}-5a-6} by multiplying \frac{3a^{2}+a-2}{4a^{2}+7a+3} by the reciprocal of \frac{3a^{2}-8a+4}{4a^{2}-5a-6}.

$$\frac{\left(3a^{2}+a-2\right)\left(4a^{2}-5a-6\right)}{\left(4a^{2}+7a+3\right)\left(3a^{2}-8a+4\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-2\right)\left(3a-2\right)\left(a+1\right)\left(4a+3\right)}{\left(a-2\right)\left(3a-2\right)\left(a+1\right)\left(4a+3\right)}$$

Cancel out \left(a-2\right)\left(3a-2\right)\left(a+1\right)\left(4a+3\right) in both numerator and denominator.

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Factor

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