Solve 3/y-1-y+2/y^2-y

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

Evaluate

$$\frac{2}{y}$$

Short Solution Steps

Factor y^{2}-y.

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

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

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

Since \frac{3y}{y\left(y-1\right)} and \frac{y+2}{y\left(y-1\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3y-\left(y+2\right).

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

Combine like terms in 3y-y-2.

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

Factor the expressions that are not already factored in \frac{2y-2}{y\left(y-1\right)}.

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

Cancel out y-1 in both numerator and denominator.

$$\frac{2}{y}$$

Expand

$$\frac{2}{y}$$

Short Solution Steps

Factor y^{2}-y.

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

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

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

Since \frac{3y}{y\left(y-1\right)} and \frac{y+2}{y\left(y-1\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3y-\left(y+2\right).

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

Combine like terms in 3y-y-2.

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

Factor the expressions that are not already factored in \frac{2y-2}{y\left(y-1\right)}.

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

Cancel out y-1 in both numerator and denominator.

$$\frac{2}{y}$$