Solve 3mn(1/m+1/n)

$$3 m n ( \frac { 1 } { m } + \frac { 1 } { n } )$$

Evaluate

$$3\left(m+n\right)$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m and n is mn. Multiply \frac{1}{m} times \frac{n}{n}. Multiply \frac{1}{n} times \frac{m}{m}.

$$3mn\left(\frac{n}{mn}+\frac{m}{mn}\right)$$

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

$$3mn\times \frac{n+m}{mn}$$

Express 3\times \frac{n+m}{mn} as a single fraction.

$$\frac{3\left(n+m\right)}{mn}mn$$

Use the distributive property to multiply 3 by n+m.

$$\frac{3n+3m}{mn}mn$$

Express \frac{3n+3m}{mn}m as a single fraction.

$$\frac{\left(3n+3m\right)m}{mn}n$$

Cancel out m in both numerator and denominator.

$$\frac{3m+3n}{n}n$$

Cancel out n and n.

$$3m+3n$$

Expand

$$3m+3n$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m and n is mn. Multiply \frac{1}{m} times \frac{n}{n}. Multiply \frac{1}{n} times \frac{m}{m}.

$$3mn\left(\frac{n}{mn}+\frac{m}{mn}\right)$$

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

$$3mn\times \frac{n+m}{mn}$$

Express 3\times \frac{n+m}{mn} as a single fraction.

$$\frac{3\left(n+m\right)}{mn}mn$$

Use the distributive property to multiply 3 by n+m.

$$\frac{3n+3m}{mn}mn$$

Express \frac{3n+3m}{mn}m as a single fraction.

$$\frac{\left(3n+3m\right)m}{mn}n$$

Cancel out m in both numerator and denominator.

$$\frac{3m+3n}{n}n$$

Cancel out n and n.

$$3m+3n$$