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

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

Evaluate

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Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-2x}{x^{2}-4x+4}.

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

Cancel out x-2 in both numerator and denominator.

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

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

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

Combine like terms in x+2-x.

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

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

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

Combine like terms in 2+x-4.

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

Cancel out x-2 in both numerator and denominator.

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Factor

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