Solve left(x^2+4/x-4right)divx^2-4/2x

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

Evaluate

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

Short Solution Steps

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

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

Since \frac{x^{2}+4}{x} and \frac{4x}{x} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-2 in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

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

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

Since \frac{x^{2}+4}{x} and \frac{4x}{x} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-2 in both numerator and denominator.

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

Expand the expression.

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