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

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

Evaluate

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

Short Solution Steps

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

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

Since \frac{x-2}{x-2} and \frac{1}{x-2} have the same denominator, add them by adding their numerators.

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

Combine like terms in x-2+1.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-4}{x-4}.

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

Since \frac{x-4}{x-4} and \frac{2}{x-4} have the same denominator, add them by adding their numerators.

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

Combine like terms in x-4+2.

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

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

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

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

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

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

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

Do the multiplications in x-2-\left(x-4\right).

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

Combine like terms in x-2-x+4.

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

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

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

Cancel out x-2 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

Since \frac{x-2}{x-2} and \frac{1}{x-2} have the same denominator, add them by adding their numerators.

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

Combine like terms in x-2+1.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-4}{x-4}.

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

Since \frac{x-4}{x-4} and \frac{2}{x-4} have the same denominator, add them by adding their numerators.

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

Combine like terms in x-4+2.

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

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

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

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

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

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

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

Do the multiplications in x-2-\left(x-4\right).

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

Combine like terms in x-2-x+4.

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

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

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

Cancel out x-2 in both numerator and denominator.

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