Solve 2-y/y-1div(y+1-3/y-1)

$$\frac { 2 - y } { y - 1 } \div ( y + 1 - \frac { 3 } { y - 1 } )$$

Evaluate

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

Short Solution Steps

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

$$\frac{\frac{2-y}{y-1}}{\frac{\left(y+1\right)\left(y-1\right)}{y-1}-\frac{3}{y-1}}$$

Since \frac{\left(y+1\right)\left(y-1\right)}{y-1} and \frac{3}{y-1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2-y}{y-1}}{\frac{\left(y+1\right)\left(y-1\right)-3}{y-1}}$$

Do the multiplications in \left(y+1\right)\left(y-1\right)-3.

$$\frac{\frac{2-y}{y-1}}{\frac{y^{2}-y+y-1-3}{y-1}}$$

Combine like terms in y^{2}-y+y-1-3.

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

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

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

Cancel out y-1 in both numerator and denominator.

$$\frac{-y+2}{y^{2}-4}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in 2-y.

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

Cancel out y-2 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

$$\frac{\frac{2-y}{y-1}}{\frac{\left(y+1\right)\left(y-1\right)}{y-1}-\frac{3}{y-1}}$$

Since \frac{\left(y+1\right)\left(y-1\right)}{y-1} and \frac{3}{y-1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2-y}{y-1}}{\frac{\left(y+1\right)\left(y-1\right)-3}{y-1}}$$

Do the multiplications in \left(y+1\right)\left(y-1\right)-3.

$$\frac{\frac{2-y}{y-1}}{\frac{y^{2}-y+y-1-3}{y-1}}$$

Combine like terms in y^{2}-y+y-1-3.

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

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

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

Cancel out y-1 in both numerator and denominator.

$$\frac{-y+2}{y^{2}-4}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in 2-y.

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

Cancel out y-2 in both numerator and denominator.

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