Solve n^2+3n+2/6-3n+n-2*8n^2/n+1

$$\frac { n ^ { 2 } + 3 n + 2 } { 6 - 3 n + n - 2 } \cdot \frac { 8 n ^ { 2 } } { n + 1 }$$

Evaluate

$$\frac{4\left(n+2\right)n^{2}}{2-n}$$

Short Solution Steps

Combine -3n and n to get -2n.

$$\frac{n^{2}+3n+2}{6-2n-2}\times \frac{8n^{2}}{n+1}$$

Subtract 2 from 6 to get 4.

$$\frac{n^{2}+3n+2}{4-2n}\times \frac{8n^{2}}{n+1}$$

Multiply \frac{n^{2}+3n+2}{4-2n} times \frac{8n^{2}}{n+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(n^{2}+3n+2\right)\times 8n^{2}}{\left(4-2n\right)\left(n+1\right)}$$

Factor the expressions that are not already factored.

$$\frac{8\left(n+1\right)\left(n+2\right)n^{2}}{2\left(n+1\right)\left(-n+2\right)}$$

Cancel out 2\left(n+1\right) in both numerator and denominator.

$$\frac{4\left(n+2\right)n^{2}}{-n+2}$$

Expand the expression.

$$\frac{4n^{3}+8n^{2}}{-n+2}$$

Expand

$$-\frac{4\left(n^{3}+2n^{2}\right)}{n-2}$$

Short Solution Steps

Combine -3n and n to get -2n.

$$\frac{n^{2}+3n+2}{6-2n-2}\times \frac{8n^{2}}{n+1}$$

Subtract 2 from 6 to get 4.

$$\frac{n^{2}+3n+2}{4-2n}\times \frac{8n^{2}}{n+1}$$

Multiply \frac{n^{2}+3n+2}{4-2n} times \frac{8n^{2}}{n+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(n^{2}+3n+2\right)\times 8n^{2}}{\left(4-2n\right)\left(n+1\right)}$$

Factor the expressions that are not already factored.

$$\frac{8\left(n+1\right)\left(n+2\right)n^{2}}{2\left(n+1\right)\left(-n+2\right)}$$

Cancel out 2\left(n+1\right) in both numerator and denominator.

$$\frac{4\left(n+2\right)n^{2}}{-n+2}$$

Expand the expression.

$$\frac{4n^{3}+8n^{2}}{-n+2}$$