Solve (4/x-x):(1/x+1/2)

$$( \frac { 4 } { x } - x ) : ( \frac { 1 } { x } + \frac { 1 } { 2 } )$$

Evaluate

$$4-2x$$

Short Solution Steps

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

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

Since \frac{4}{x} and \frac{xx}{x} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 4-xx.

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

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

$$\frac{\frac{4-x^{2}}{x}}{\frac{2}{2x}+\frac{x}{2x}}$$

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

$$\frac{\frac{4-x^{2}}{x}}{\frac{2+x}{2x}}$$

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

$$\frac{\left(4-x^{2}\right)\times 2x}{x\left(2+x\right)}$$

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -2-x.

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

Cancel out x+2 in both numerator and denominator.

$$-2\left(x-2\right)$$

Expand the expression.

$$-2x+4$$

Expand

$$4-2x$$

Short Solution Steps

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

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

Since \frac{4}{x} and \frac{xx}{x} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 4-xx.

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

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

$$\frac{\frac{4-x^{2}}{x}}{\frac{2}{2x}+\frac{x}{2x}}$$

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

$$\frac{\frac{4-x^{2}}{x}}{\frac{2+x}{2x}}$$

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

$$\frac{\left(4-x^{2}\right)\times 2x}{x\left(2+x\right)}$$

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -2-x.

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

Cancel out x+2 in both numerator and denominator.

$$-2\left(x-2\right)$$

Expand the expression.

$$-2x+4$$