Solve v^2+6v+5/8v^5/frac{v+5{4v^2}}

$$\frac { \frac { v ^ { 2 } + 6 v + 5 } { 8 v ^ { 5 } } } { \frac { v + 5 } { 4 v ^ { 2 } } }$$

Evaluate

$$\frac{v+1}{2v^{3}}$$

Short Solution Steps

Divide \frac{v^{2}+6v+5}{8v^{5}} by \frac{v+5}{4v^{2}} by multiplying \frac{v^{2}+6v+5}{8v^{5}} by the reciprocal of \frac{v+5}{4v^{2}}.

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

Cancel out 4v^{2} in both numerator and denominator.

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

Factor the expressions that are not already factored.

$$\frac{\left(v+1\right)\left(v+5\right)}{2\left(v+5\right)v^{3}}$$

Cancel out v+5 in both numerator and denominator.

$$\frac{v+1}{2v^{3}}$$

Expand

$$\frac{v+1}{2v^{3}}$$

Short Solution Steps

Divide \frac{v^{2}+6v+5}{8v^{5}} by \frac{v+5}{4v^{2}} by multiplying \frac{v^{2}+6v+5}{8v^{5}} by the reciprocal of \frac{v+5}{4v^{2}}.

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

Cancel out 4v^{2} in both numerator and denominator.

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

Factor the expressions that are not already factored.

$$\frac{\left(v+1\right)\left(v+5\right)}{2\left(v+5\right)v^{3}}$$

Cancel out v+5 in both numerator and denominator.

$$\frac{v+1}{2v^{3}}$$