Solve -3/y+1+y-1/y

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y+1 and y is y\left(y+1\right). Multiply \frac{-3}{y+1} times \frac{y}{y}. Multiply \frac{y-1}{y} times \frac{y+1}{y+1}.

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

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

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

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

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

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

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

Expand y\left(y+1\right).

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y+1 and y is y\left(y+1\right). Multiply \frac{-3}{y+1} times \frac{y}{y}. Multiply \frac{y-1}{y} times \frac{y+1}{y+1}.

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

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

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

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

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

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

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

Expand y\left(y+1\right).

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