Solve x^2-4x+4/x^2-2x/(x-4/x)

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

Evaluate

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

Short Solution Steps

Express \frac{\frac{x^{2}-4x+4}{x^{2}-2x}}{x-\frac{4}{x}} as a single fraction.

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

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

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

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

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

Do the multiplications in xx-4.

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

Express \left(x^{2}-2x\right)\times \frac{x^{2}-4}{x} as a single fraction.

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

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

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

Factor the expressions that are not already factored.

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

Cancel out x\left(x-2\right)^{2} in both numerator and denominator.

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

Expand

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

Short Solution Steps

Express \frac{\frac{x^{2}-4x+4}{x^{2}-2x}}{x-\frac{4}{x}} as a single fraction.

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

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

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

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

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

Do the multiplications in xx-4.

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

Express \left(x^{2}-2x\right)\times \frac{x^{2}-4}{x} as a single fraction.

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

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

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

Factor the expressions that are not already factored.

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

Cancel out x\left(x-2\right)^{2} in both numerator and denominator.

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