Solve 2/6n^3-6n^2-2

$$\frac{ 2 }{ 6 { n }^{ 3 } -6 { n }^{ 2 } } -2$$

Evaluate

$$\frac{1+6n^{2}-6n^{3}}{3\left(n-1\right)n^{2}}$$

Short Solution Steps

Factor 6n^{3}-6n^{2}.

$$\frac{2}{6\left(n-1\right)n^{2}}-2$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{6\left(n-1\right)n^{2}}{6\left(n-1\right)n^{2}}.

$$\frac{2}{6\left(n-1\right)n^{2}}-\frac{2\times 6\left(n-1\right)n^{2}}{6\left(n-1\right)n^{2}}$$

Since \frac{2}{6\left(n-1\right)n^{2}} and \frac{2\times 6\left(n-1\right)n^{2}}{6\left(n-1\right)n^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-2\times 6\left(n-1\right)n^{2}}{6\left(n-1\right)n^{2}}$$

Do the multiplications in 2-2\times 6\left(n-1\right)n^{2}.

$$\frac{2-12n^{3}+12n^{2}}{6\left(n-1\right)n^{2}}$$

Factor the expressions that are not already factored in \frac{2-12n^{3}+12n^{2}}{6\left(n-1\right)n^{2}}.

$$\frac{2\left(-6n^{3}+6n^{2}+1\right)}{6\left(n-1\right)n^{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-6n^{3}+6n^{2}+1}{3\left(n-1\right)n^{2}}$$

Expand 3\left(n-1\right)n^{2}.

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

Factor

$$\frac{1+6n^{2}-6n^{3}}{3\left(n-1\right)n^{2}}$$