Solve 2-(n+1)(2n+1)/6n^2

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

Evaluate

$$\frac{5}{3}-\frac{1}{2n}-\frac{1}{6n^{2}}$$

Short Solution Steps

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

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

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

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

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

$$\frac{12n^{2}-2n^{2}-n-2n-1}{6n^{2}}$$

Combine like terms in 12n^{2}-2n^{2}-n-2n-1.

$$\frac{10n^{2}-3n-1}{6n^{2}}$$

Expand

$$\frac{5}{3}-\frac{1}{2n}-\frac{1}{6n^{2}}$$

Short Solution Steps

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

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

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

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

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

$$\frac{12n^{2}-2n^{2}-n-2n-1}{6n^{2}}$$

Combine like terms in 12n^{2}-2n^{2}-n-2n-1.

$$\frac{10n^{2}-3n-1}{6n^{2}}$$