Solve y-6/y^2+2y-4/y+2

$$\frac { y - 6 } { y ^ { 2 } + 2 y } - \frac { 4 } { y + 2 }$$

Evaluate

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

Short Solution Steps

Factor y^{2}+2y.

$$\frac{y-6}{y\left(y+2\right)}-\frac{4}{y+2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y\left(y+2\right) and y+2 is y\left(y+2\right). Multiply \frac{4}{y+2} times \frac{y}{y}.

$$\frac{y-6}{y\left(y+2\right)}-\frac{4y}{y\left(y+2\right)}$$

Since \frac{y-6}{y\left(y+2\right)} and \frac{4y}{y\left(y+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y-6-4y}{y\left(y+2\right)}$$

Combine like terms in y-6-4y.

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

Factor the expressions that are not already factored in \frac{-3y-6}{y\left(y+2\right)}.

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

Extract the negative sign in -2-y.

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

Cancel out y+2 in both numerator and denominator.

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

Expand

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

Short Solution Steps

Factor y^{2}+2y.

$$\frac{y-6}{y\left(y+2\right)}-\frac{4}{y+2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y\left(y+2\right) and y+2 is y\left(y+2\right). Multiply \frac{4}{y+2} times \frac{y}{y}.

$$\frac{y-6}{y\left(y+2\right)}-\frac{4y}{y\left(y+2\right)}$$

Since \frac{y-6}{y\left(y+2\right)} and \frac{4y}{y\left(y+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y-6-4y}{y\left(y+2\right)}$$

Combine like terms in y-6-4y.

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

Factor the expressions that are not already factored in \frac{-3y-6}{y\left(y+2\right)}.

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

Extract the negative sign in -2-y.

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

Cancel out y+2 in both numerator and denominator.

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