Solve (16a ^ 3 - 20a ^ 2 - 45a - 9)/((4a ^ 2 - 9)(2a ^ 2 - 2a - 3)) / ((a + 1)/(2a - 3)) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{16a^{3}-20a^{2}-45a-9}{(4a^{2}-9)(2a^{2}-2a-3)}\div\frac{a+1}{2a-3}$$

Evaluate

$-\frac{16a^{2}-36a-9}{\left(2a+3\right)\left(3+2a-2a^{2}\right)}$

Short Solution Steps

Divide $\frac{16a^{3}-20a^{2}-45a-9}{\left(4a^{2}-9\right)\left(2a^{2}-2a-3\right)}$ by $\frac{a+1}{2a-3}$ by multiplying $\frac{16a^{3}-20a^{2}-45a-9}{\left(4a^{2}-9\right)\left(2a^{2}-2a-3\right)}$ by the reciprocal of $\frac{a+1}{2a-3}$.

$$\frac{\left(16a^{3}-20a^{2}-45a-9\right)\left(2a-3\right)}{\left(4a^{2}-9\right)\left(2a^{2}-2a-3\right)\left(a+1\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(2a-3\right)\left(a+1\right)\left(16a^{2}-36a-9\right)}{2\left(2a-3\right)\left(a+1\right)\left(2a+3\right)\left(a-\left(-\frac{1}{2}\sqrt{7}+\frac{1}{2}\right)\right)\left(a-\left(\frac{1}{2}\sqrt{7}+\frac{1}{2}\right)\right)}$$

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

$$\frac{16a^{2}-36a-9}{2\left(2a+3\right)\left(a-\left(-\frac{1}{2}\sqrt{7}+\frac{1}{2}\right)\right)\left(a-\left(\frac{1}{2}\sqrt{7}+\frac{1}{2}\right)\right)}$$

Expand the expression.

$$\frac{16a^{2}-36a-9}{4a^{3}+2a^{2}-12a-9}$$

Expand

$\frac{16a^{2}-36a-9}{\left(2a+3\right)\left(2a^{2}-2a-3\right)}$

Short Solution Steps

Divide $\frac{16a^{3}-20a^{2}-45a-9}{\left(4a^{2}-9\right)\left(2a^{2}-2a-3\right)}$ by $\frac{a+1}{2a-3}$ by multiplying $\frac{16a^{3}-20a^{2}-45a-9}{\left(4a^{2}-9\right)\left(2a^{2}-2a-3\right)}$ by the reciprocal of $\frac{a+1}{2a-3}$.

$$\frac{\left(16a^{3}-20a^{2}-45a-9\right)\left(2a-3\right)}{\left(4a^{2}-9\right)\left(2a^{2}-2a-3\right)\left(a+1\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(2a-3\right)\left(a+1\right)\left(16a^{2}-36a-9\right)}{2\left(2a-3\right)\left(a+1\right)\left(2a+3\right)\left(a-\left(-\frac{1}{2}\sqrt{7}+\frac{1}{2}\right)\right)\left(a-\left(\frac{1}{2}\sqrt{7}+\frac{1}{2}\right)\right)}$$

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

$$\frac{16a^{2}-36a-9}{2\left(2a+3\right)\left(a-\left(-\frac{1}{2}\sqrt{7}+\frac{1}{2}\right)\right)\left(a-\left(\frac{1}{2}\sqrt{7}+\frac{1}{2}\right)\right)}$$

Expand the expression.

$$\frac{16a^{2}-36a-9}{4a^{3}+2a^{2}-12a-9}$$