Solve x+1/2/4+frac{2{x}}

$$\frac { x + \frac { 1 } { 2 } } { 4 + \frac { 2 } { x } }$$

Evaluate

$$\frac{x}{4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x}{x}.

$$\frac{x+\frac{1}{2}}{\frac{4x}{x}+\frac{2}{x}}$$

Since \frac{4x}{x} and \frac{2}{x} have the same denominator, add them by adding their numerators.

$$\frac{x+\frac{1}{2}}{\frac{4x+2}{x}}$$

Divide x+\frac{1}{2} by \frac{4x+2}{x} by multiplying x+\frac{1}{2} by the reciprocal of \frac{4x+2}{x}.

$$\frac{\left(x+\frac{1}{2}\right)x}{4x+2}$$

Factor the expressions that are not already factored.

$$\frac{\frac{1}{2}x\left(2x+1\right)}{2\left(2x+1\right)}$$

Cancel out 2x+1 in both numerator and denominator.

$$\frac{\frac{1}{2}x}{2}$$

Divide \frac{1}{2}x by 2 to get \frac{1}{4}x.

$$\frac{1}{4}x$$

Expand

$$\frac{x}{4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x}{x}.

$$\frac{x+\frac{1}{2}}{\frac{4x}{x}+\frac{2}{x}}$$

Since \frac{4x}{x} and \frac{2}{x} have the same denominator, add them by adding their numerators.

$$\frac{x+\frac{1}{2}}{\frac{4x+2}{x}}$$

Divide x+\frac{1}{2} by \frac{4x+2}{x} by multiplying x+\frac{1}{2} by the reciprocal of \frac{4x+2}{x}.

$$\frac{\left(x+\frac{1}{2}\right)x}{4x+2}$$

Factor the expressions that are not already factored.

$$\frac{\frac{1}{2}x\left(2x+1\right)}{2\left(2x+1\right)}$$

Cancel out 2x+1 in both numerator and denominator.

$$\frac{\frac{1}{2}x}{2}$$

Divide \frac{1}{2}x by 2 to get \frac{1}{4}x.

$$\frac{1}{4}x$$