Solve 1/3x+2/y/frac{2{x}}

$$\frac { \frac { 1 } { 3 x } + \frac { 2 } { y } } { \frac { 2 } { x } }$$

Evaluate

$$\frac{x}{y}+\frac{1}{6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x and y is 3xy. Multiply \frac{1}{3x} times \frac{y}{y}. Multiply \frac{2}{y} times \frac{3x}{3x}.

$$\frac{\frac{y}{3xy}+\frac{2\times 3x}{3xy}}{\frac{2}{x}}$$

Since \frac{y}{3xy} and \frac{2\times 3x}{3xy} have the same denominator, add them by adding their numerators.

$$\frac{\frac{y+2\times 3x}{3xy}}{\frac{2}{x}}$$

Do the multiplications in y+2\times 3x.

$$\frac{\frac{y+6x}{3xy}}{\frac{2}{x}}$$

Divide \frac{y+6x}{3xy} by \frac{2}{x} by multiplying \frac{y+6x}{3xy} by the reciprocal of \frac{2}{x}.

$$\frac{\left(y+6x\right)x}{3xy\times 2}$$

Cancel out x in both numerator and denominator.

$$\frac{6x+y}{2\times 3y}$$

Multiply 2 and 3 to get 6.

$$\frac{6x+y}{6y}$$

Expand

$$\frac{x}{y}+\frac{1}{6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x and y is 3xy. Multiply \frac{1}{3x} times \frac{y}{y}. Multiply \frac{2}{y} times \frac{3x}{3x}.

$$\frac{\frac{y}{3xy}+\frac{2\times 3x}{3xy}}{\frac{2}{x}}$$

Since \frac{y}{3xy} and \frac{2\times 3x}{3xy} have the same denominator, add them by adding their numerators.

$$\frac{\frac{y+2\times 3x}{3xy}}{\frac{2}{x}}$$

Do the multiplications in y+2\times 3x.

$$\frac{\frac{y+6x}{3xy}}{\frac{2}{x}}$$

Divide \frac{y+6x}{3xy} by \frac{2}{x} by multiplying \frac{y+6x}{3xy} by the reciprocal of \frac{2}{x}.

$$\frac{\left(y+6x\right)x}{3xy\times 2}$$

Cancel out x in both numerator and denominator.

$$\frac{6x+y}{2\times 3y}$$

Multiply 2 and 3 to get 6.

$$\frac{6x+y}{6y}$$