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

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x^{2}}{x^{2}}.

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

Since \frac{1}{x^{2}} and \frac{4x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Since \frac{1}{x} and \frac{2x}{x} have the same denominator, subtract them by subtracting their numerators.

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

Divide \frac{1-4x^{2}}{x^{2}} by \frac{1-2x}{x} by multiplying \frac{1-4x^{2}}{x^{2}} by the reciprocal of \frac{1-2x}{x}.

$$\frac{\left(1-4x^{2}\right)x}{x^{2}\left(1-2x\right)}$$

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -1+2x.

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

Cancel out -2x+1 in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x^{2}}{x^{2}}.

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

Since \frac{1}{x^{2}} and \frac{4x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Since \frac{1}{x} and \frac{2x}{x} have the same denominator, subtract them by subtracting their numerators.

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

Divide \frac{1-4x^{2}}{x^{2}} by \frac{1-2x}{x} by multiplying \frac{1-4x^{2}}{x^{2}} by the reciprocal of \frac{1-2x}{x}.

$$\frac{\left(1-4x^{2}\right)x}{x^{2}\left(1-2x\right)}$$

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -1+2x.

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

Cancel out -2x+1 in both numerator and denominator.

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

Expand the expression.

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