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

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

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}.

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

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

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

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

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

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

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

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

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

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.

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

Extract the negative sign in 2-x.

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

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}.

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

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

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

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

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

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

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

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

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

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.

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

Extract the negative sign in 2-x.

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

Cancel out x-2 in both numerator and denominator.

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