Solve x^2-4x+4/x^2+2xdiv(4/x+2-1)

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+2}{x+2}.

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

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

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

Do the multiplications in 4-\left(x+2\right).

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

Combine like terms in 4-x-2.

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

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

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

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+2}{x+2}.

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

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

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

Do the multiplications in 4-\left(x+2\right).

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

Combine like terms in 4-x-2.

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

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

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

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

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

Expand the expression.

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