Solve 9/y-2-3/y

$$\frac { 9 } { y - 2 } - \frac { 3 } { y }$$

Evaluate

$$\frac{6\left(y+1\right)}{y\left(y-2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y-2 and y is y\left(y-2\right). Multiply \frac{9}{y-2} times \frac{y}{y}. Multiply \frac{3}{y} times \frac{y-2}{y-2}.

$$\frac{9y}{y\left(y-2\right)}-\frac{3\left(y-2\right)}{y\left(y-2\right)}$$

Since \frac{9y}{y\left(y-2\right)} and \frac{3\left(y-2\right)}{y\left(y-2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9y-3\left(y-2\right)}{y\left(y-2\right)}$$

Do the multiplications in 9y-3\left(y-2\right).

$$\frac{9y-3y+6}{y\left(y-2\right)}$$

Combine like terms in 9y-3y+6.

$$\frac{6y+6}{y\left(y-2\right)}$$

Expand y\left(y-2\right).

$$\frac{6y+6}{y^{2}-2y}$$

Factor

$$\frac{6\left(y+1\right)}{y\left(y-2\right)}$$