Solve y+1/y-2/1+frac{1{y-2}}

$$\frac { y + \frac { 1 } { y - 2 } } { 1 + \frac { 1 } { y - 2 } }$$

Evaluate

$$y-1$$

Short Solution Steps

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

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

Since \frac{y\left(y-2\right)}{y-2} and \frac{1}{y-2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in y\left(y-2\right)+1.

$$\frac{\frac{y^{2}-2y+1}{y-2}}{1+\frac{1}{y-2}}$$

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

$$\frac{\frac{y^{2}-2y+1}{y-2}}{\frac{y-2}{y-2}+\frac{1}{y-2}}$$

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

$$\frac{\frac{y^{2}-2y+1}{y-2}}{\frac{y-2+1}{y-2}}$$

Combine like terms in y-2+1.

$$\frac{\frac{y^{2}-2y+1}{y-2}}{\frac{y-1}{y-2}}$$

Divide \frac{y^{2}-2y+1}{y-2} by \frac{y-1}{y-2} by multiplying \frac{y^{2}-2y+1}{y-2} by the reciprocal of \frac{y-1}{y-2}.

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

Cancel out y-2 in both numerator and denominator.

$$\frac{y^{2}-2y+1}{y-1}$$

Factor the expressions that are not already factored.

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

Cancel out y-1 in both numerator and denominator.

$$y-1$$

Expand

$$y-1$$

Short Solution Steps

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

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

Since \frac{y\left(y-2\right)}{y-2} and \frac{1}{y-2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in y\left(y-2\right)+1.

$$\frac{\frac{y^{2}-2y+1}{y-2}}{1+\frac{1}{y-2}}$$

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

$$\frac{\frac{y^{2}-2y+1}{y-2}}{\frac{y-2}{y-2}+\frac{1}{y-2}}$$

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

$$\frac{\frac{y^{2}-2y+1}{y-2}}{\frac{y-2+1}{y-2}}$$

Combine like terms in y-2+1.

$$\frac{\frac{y^{2}-2y+1}{y-2}}{\frac{y-1}{y-2}}$$

Divide \frac{y^{2}-2y+1}{y-2} by \frac{y-1}{y-2} by multiplying \frac{y^{2}-2y+1}{y-2} by the reciprocal of \frac{y-1}{y-2}.

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

Cancel out y-2 in both numerator and denominator.

$$\frac{y^{2}-2y+1}{y-1}$$

Factor the expressions that are not already factored.

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

Cancel out y-1 in both numerator and denominator.

$$y-1$$