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

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

Evaluate

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

Short Solution Steps

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

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

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

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

Combine like terms in y-1-y.

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

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

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

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

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

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

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

Combine like terms in y-y-1.

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

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

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

Cancel out -1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

Combine like terms in y-1-y.

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

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

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

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

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

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

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

Combine like terms in y-y-1.

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

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

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

Cancel out -1 in both numerator and denominator.

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