Solve y^2+6y/y-3-2y-33/3-y

$$\frac { y ^ { 2 } + 6 y } { y - 3 } - \frac { 2 y - 33 } { 3 - y }$$

Evaluate

$$y+11$$

Short Solution Steps

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{2y-33}{3-y} times \frac{-1}{-1}.

$$\frac{y^{2}+6y}{y-3}-\frac{-\left(2y-33\right)}{y-3}$$

Since \frac{y^{2}+6y}{y-3} and \frac{-\left(2y-33\right)}{y-3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y^{2}+6y-\left(-\left(2y-33\right)\right)}{y-3}$$

Do the multiplications in y^{2}+6y-\left(-\left(2y-33\right)\right).

$$\frac{y^{2}+6y+2y-33}{y-3}$$

Combine like terms in y^{2}+6y+2y-33.

$$\frac{y^{2}+8y-33}{y-3}$$

Factor the expressions that are not already factored in \frac{y^{2}+8y-33}{y-3}.

$$\frac{\left(y-3\right)\left(y+11\right)}{y-3}$$

Cancel out y-3 in both numerator and denominator.

$$y+11$$

Expand

$$y+11$$

Short Solution Steps

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{2y-33}{3-y} times \frac{-1}{-1}.

$$\frac{y^{2}+6y}{y-3}-\frac{-\left(2y-33\right)}{y-3}$$

Since \frac{y^{2}+6y}{y-3} and \frac{-\left(2y-33\right)}{y-3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y^{2}+6y-\left(-\left(2y-33\right)\right)}{y-3}$$

Do the multiplications in y^{2}+6y-\left(-\left(2y-33\right)\right).

$$\frac{y^{2}+6y+2y-33}{y-3}$$

Combine like terms in y^{2}+6y+2y-33.

$$\frac{y^{2}+8y-33}{y-3}$$

Factor the expressions that are not already factored in \frac{y^{2}+8y-33}{y-3}.

$$\frac{\left(y-3\right)\left(y+11\right)}{y-3}$$

Cancel out y-3 in both numerator and denominator.

$$y+11$$