Solve y+2/y^2-y-6+2/3-y

$$\frac { y + 2 } { y ^ { 2 } - y - 6 } + \frac { 2 } { 3 - y }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{y+2}{y^{2}-y-6}.

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

Cancel out y+2 in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y-3 and 3-y is y-3. Multiply \frac{2}{3-y} times \frac{-1}{-1}.

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

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

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

Do the multiplications in 1+2\left(-1\right).

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

Do the calculations in 1-2.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{y+2}{y^{2}-y-6}.

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

Cancel out y+2 in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y-3 and 3-y is y-3. Multiply \frac{2}{3-y} times \frac{-1}{-1}.

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

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

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

Do the multiplications in 1+2\left(-1\right).

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

Do the calculations in 1-2.

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