Solve 1/5x+2/x-1/2y

$$\frac { 1 } { 5 x } + \frac { 2 } { x } - \frac { 1 } { 2 y }$$

Evaluate

$$\frac{22y-5x}{10xy}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5x and x is 5x. Multiply \frac{2}{x} times \frac{5}{5}.

$$\frac{1}{5x}+\frac{2\times 5}{5x}-\frac{1}{2y}$$

Since \frac{1}{5x} and \frac{2\times 5}{5x} have the same denominator, add them by adding their numerators.

$$\frac{1+2\times 5}{5x}-\frac{1}{2y}$$

Do the multiplications in 1+2\times 5.

$$\frac{1+10}{5x}-\frac{1}{2y}$$

Do the calculations in 1+10.

$$\frac{11}{5x}-\frac{1}{2y}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5x and 2y is 10xy. Multiply \frac{11}{5x} times \frac{2y}{2y}. Multiply \frac{1}{2y} times \frac{5x}{5x}.

$$\frac{11\times 2y}{10xy}-\frac{5x}{10xy}$$

Since \frac{11\times 2y}{10xy} and \frac{5x}{10xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11\times 2y-5x}{10xy}$$

Do the multiplications in 11\times 2y-5x.

$$\frac{22y-5x}{10xy}$$

Factor

$$\frac{-\frac{5x}{y}+22}{10x}$$