Solve x/3+1/6+2/5

$$\frac { x } { 3 } + \frac { 1 } { 6 } + \frac { 2 } { 5 }$$

Evaluate

$$\frac{x}{3}+\frac{17}{30}$$

Solution Steps

Least common multiple of 6 and 5 is 30. Convert \frac{1}{6} and \frac{2}{5} to fractions with denominator 30.

$$\frac{x}{3}+\frac{5}{30}+\frac{12}{30}$$

Since \frac{5}{30} and \frac{12}{30} have the same denominator, add them by adding their numerators.

$$\frac{x}{3}+\frac{5+12}{30}$$

Add 5 and 12 to get 17.

$$\frac{x}{3}+\frac{17}{30}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 30 is 30. Multiply \frac{x}{3} times \frac{10}{10}.

$$\frac{10x}{30}+\frac{17}{30}$$

Since \frac{10x}{30} and \frac{17}{30} have the same denominator, add them by adding their numerators.

$$\frac{10x+17}{30}$$

Factor

$$\frac{10x+17}{30}$$

Solution Steps

Factor out \frac{1}{30}.

$$\frac{10x+17}{30}$$

Consider 10x+5+12. Multiply and combine like terms.

$$10x+17$$

Rewrite the complete factored expression.

$$\frac{10x+17}{30}$$