Solve 2+1/n/frac{1{2n^2}}

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

Evaluate

$$2n\left(2n+1\right)$$

Solution Steps

Divide 2+\frac{1}{n} by \frac{1}{2n^{2}} by multiplying 2+\frac{1}{n} by the reciprocal of \frac{1}{2n^{2}}.

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

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

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

Since \frac{2n}{n} and \frac{1}{n} have the same denominator, add them by adding their numerators.

$$\frac{2n+1}{n}\times 2n^{2}$$

Express \frac{2n+1}{n}\times 2 as a single fraction.

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

Express \frac{\left(2n+1\right)\times 2}{n}n^{2} as a single fraction.

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

Cancel out n in both numerator and denominator.

$$2n\left(2n+1\right)$$

Use the distributive property to multiply 2n by 2n+1.

$$4n^{2}+2n$$

Expand

$$4n^{2}+2n$$

Solution Steps

Divide 2+\frac{1}{n} by \frac{1}{2n^{2}} by multiplying 2+\frac{1}{n} by the reciprocal of \frac{1}{2n^{2}}.

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

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

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

Since \frac{2n}{n} and \frac{1}{n} have the same denominator, add them by adding their numerators.

$$\frac{2n+1}{n}\times 2n^{2}$$

Express \frac{2n+1}{n}\times 2 as a single fraction.

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

Express \frac{\left(2n+1\right)\times 2}{n}n^{2} as a single fraction.

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

Cancel out n in both numerator and denominator.

$$2n\left(2n+1\right)$$

Use the distributive property to multiply 2n by 2n+1.

$$4n^{2}+2n$$