Solve v-8/2v^2-7v-30-4v

$$\frac { v - 8 } { 2 v ^ { 2 } - 7 v - 30 } - 4 v$$

Evaluate

$$\frac{-8v^{3}+28v^{2}+121v-8}{\left(v-6\right)\left(2v+5\right)}$$

Short Solution Steps

Factor 2v^{2}-7v-30.

$$\frac{v-8}{\left(v-6\right)\left(2v+5\right)}-4v$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -4v times \frac{\left(v-6\right)\left(2v+5\right)}{\left(v-6\right)\left(2v+5\right)}.

$$\frac{v-8}{\left(v-6\right)\left(2v+5\right)}+\frac{-4v\left(v-6\right)\left(2v+5\right)}{\left(v-6\right)\left(2v+5\right)}$$

Since \frac{v-8}{\left(v-6\right)\left(2v+5\right)} and \frac{-4v\left(v-6\right)\left(2v+5\right)}{\left(v-6\right)\left(2v+5\right)} have the same denominator, add them by adding their numerators.

$$\frac{v-8-4v\left(v-6\right)\left(2v+5\right)}{\left(v-6\right)\left(2v+5\right)}$$

Do the multiplications in v-8-4v\left(v-6\right)\left(2v+5\right).

$$\frac{v-8-8v^{3}-20v^{2}+48v^{2}+120v}{\left(v-6\right)\left(2v+5\right)}$$

Combine like terms in v-8-8v^{3}-20v^{2}+48v^{2}+120v.

$$\frac{121v-8-8v^{3}+28v^{2}}{\left(v-6\right)\left(2v+5\right)}$$

Expand \left(v-6\right)\left(2v+5\right).

$$\frac{121v-8-8v^{3}+28v^{2}}{2v^{2}-7v-30}$$

Expand

$$\frac{-8v^{3}+28v^{2}+121v-8}{2v^{2}-7v-30}$$

Short Solution Steps

Factor 2v^{2}-7v-30.

$$\frac{v-8}{\left(v-6\right)\left(2v+5\right)}-4v$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -4v times \frac{\left(v-6\right)\left(2v+5\right)}{\left(v-6\right)\left(2v+5\right)}.

$$\frac{v-8}{\left(v-6\right)\left(2v+5\right)}+\frac{-4v\left(v-6\right)\left(2v+5\right)}{\left(v-6\right)\left(2v+5\right)}$$

Since \frac{v-8}{\left(v-6\right)\left(2v+5\right)} and \frac{-4v\left(v-6\right)\left(2v+5\right)}{\left(v-6\right)\left(2v+5\right)} have the same denominator, add them by adding their numerators.

$$\frac{v-8-4v\left(v-6\right)\left(2v+5\right)}{\left(v-6\right)\left(2v+5\right)}$$

Do the multiplications in v-8-4v\left(v-6\right)\left(2v+5\right).

$$\frac{v-8-8v^{3}-20v^{2}+48v^{2}+120v}{\left(v-6\right)\left(2v+5\right)}$$

Combine like terms in v-8-8v^{3}-20v^{2}+48v^{2}+120v.

$$\frac{121v-8-8v^{3}+28v^{2}}{\left(v-6\right)\left(2v+5\right)}$$

Expand \left(v-6\right)\left(2v+5\right).

$$\frac{121v-8-8v^{3}+28v^{2}}{2v^{2}-7v-30}$$