Solve 8x^3/2x+12*x^2+7x+6/4x^5

$$\frac { 8 x ^ { 3 } } { 2 x + 12 } \cdot \frac { x ^ { 2 } + 7 x + 6 } { 4 x ^ { 5 } }$$

Evaluate

$$\frac{x+1}{x^{2}}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{8x^{3}}{2x+12}.

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

Cancel out 2 in both numerator and denominator.

$$\frac{4x^{3}}{x+6}\times \frac{x^{2}+7x+6}{4x^{5}}$$

Multiply \frac{4x^{3}}{x+6} times \frac{x^{2}+7x+6}{4x^{5}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4x^{3}\left(x^{2}+7x+6\right)}{\left(x+6\right)\times 4x^{5}}$$

Cancel out 4x^{3} in both numerator and denominator.

$$\frac{x^{2}+7x+6}{\left(x+6\right)x^{2}}$$

Factor the expressions that are not already factored.

$$\frac{\left(x+1\right)\left(x+6\right)}{\left(x+6\right)x^{2}}$$

Cancel out x+6 in both numerator and denominator.

$$\frac{x+1}{x^{2}}$$

Expand

$$\frac{x+1}{x^{2}}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{8x^{3}}{2x+12}.

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

Cancel out 2 in both numerator and denominator.

$$\frac{4x^{3}}{x+6}\times \frac{x^{2}+7x+6}{4x^{5}}$$

Multiply \frac{4x^{3}}{x+6} times \frac{x^{2}+7x+6}{4x^{5}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4x^{3}\left(x^{2}+7x+6\right)}{\left(x+6\right)\times 4x^{5}}$$

Cancel out 4x^{3} in both numerator and denominator.

$$\frac{x^{2}+7x+6}{\left(x+6\right)x^{2}}$$

Factor the expressions that are not already factored.

$$\frac{\left(x+1\right)\left(x+6\right)}{\left(x+6\right)x^{2}}$$

Cancel out x+6 in both numerator and denominator.

$$\frac{x+1}{x^{2}}$$