Solve 2x-4/x^2-4div2x/x+2-1

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

Evaluate

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

Short Solution Steps

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

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

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

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

Cancel out 2\left(x-2\right)\left(x+2\right) in both numerator and denominator.

$$\frac{1}{x}-1$$

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

$$\frac{1}{x}-\frac{x}{x}$$

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

$$\frac{1-x}{x}$$

Expand

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

Short Solution Steps

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

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

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

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

Cancel out 2\left(x-2\right)\left(x+2\right) in both numerator and denominator.

$$\frac{1}{x}-1$$

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

$$\frac{1}{x}-\frac{x}{x}$$

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

$$\frac{1-x}{x}$$