Solve 1+2/x/1-frac{4{x^2}}

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

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