Solve 8314(2/n2+3/n2/3)

$$8314 ( 2 / n 2 + 3 / n \frac { 2 } { 3 } )$$

Evaluate

$$\frac{16628\left(n+n_{2}\right)}{nn_{2}}$$

Short Solution Steps

Multiply \frac{3}{n} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$8314\left(\frac{2}{n_{2}}+\frac{3\times 2}{n\times 3}\right)$$

Cancel out 3 in both numerator and denominator.

$$8314\left(\frac{2}{n_{2}}+\frac{2}{n}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of n_{2} and n is nn_{2}. Multiply \frac{2}{n_{2}} times \frac{n}{n}. Multiply \frac{2}{n} times \frac{n_{2}}{n_{2}}.

$$8314\left(\frac{2n}{nn_{2}}+\frac{2n_{2}}{nn_{2}}\right)$$

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

$$8314\times \frac{2n+2n_{2}}{nn_{2}}$$

Express 8314\times \frac{2n+2n_{2}}{nn_{2}} as a single fraction.

$$\frac{8314\left(2n+2n_{2}\right)}{nn_{2}}$$

Use the distributive property to multiply 8314 by 2n+2n_{2}.

$$\frac{16628n+16628n_{2}}{nn_{2}}$$

Expand

$$\frac{16628\left(n+n_{2}\right)}{nn_{2}}$$

Short Solution Steps

Multiply \frac{3}{n} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$8314\left(\frac{2}{n_{2}}+\frac{3\times 2}{n\times 3}\right)$$

Cancel out 3 in both numerator and denominator.

$$8314\left(\frac{2}{n_{2}}+\frac{2}{n}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of n_{2} and n is nn_{2}. Multiply \frac{2}{n_{2}} times \frac{n}{n}. Multiply \frac{2}{n} times \frac{n_{2}}{n_{2}}.

$$8314\left(\frac{2n}{nn_{2}}+\frac{2n_{2}}{nn_{2}}\right)$$

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

$$8314\times \frac{2n+2n_{2}}{nn_{2}}$$

Express 8314\times \frac{2n+2n_{2}}{nn_{2}} as a single fraction.

$$\frac{8314\left(2n+2n_{2}\right)}{nn_{2}}$$

Use the distributive property to multiply 8314 by 2n+2n_{2}.

$$\frac{16628n+16628n_{2}}{nn_{2}}$$