Solve x^2+2/x^2-2x-1=

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

Evaluate

$$\frac{2\left(x+1\right)}{x\left(x-2\right)}$$

Short Solution Steps

Factor x^{2}-2x.

$$\frac{x^{2}+2}{x\left(x-2\right)}-1$$

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

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

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

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

Do the multiplications in x^{2}+2-x\left(x-2\right).

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

Combine like terms in x^{2}+2-x^{2}+2x.

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

Expand x\left(x-2\right).

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

Expand

$$\frac{2\left(x+1\right)}{x^{2}-2x}$$

Short Solution Steps

Factor x^{2}-2x.

$$\frac{x^{2}+2}{x\left(x-2\right)}-1$$

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

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

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

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

Do the multiplications in x^{2}+2-x\left(x-2\right).

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

Combine like terms in x^{2}+2-x^{2}+2x.

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

Expand x\left(x-2\right).

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