Solve =(1/x)-1/(-frac{1{x})+1}

$$= \frac { ( \frac { 1 } { x } ) - 1 } { ( - \frac { 1 } { x } ) + 1 }$$

Evaluate

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Solution Steps

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

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

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

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

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

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

Since -\frac{1}{x} and \frac{x}{x} have the same denominator, add them by adding their numerators.

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

Divide \frac{1-x}{x} by \frac{-1+x}{x} by multiplying \frac{1-x}{x} by the reciprocal of \frac{-1+x}{x}.

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

Extract the negative sign in 1-x.

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

Cancel out x\left(x-1\right) in both numerator and denominator.

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Factor

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