Solve 18/y+4-3/y-frac{12{y+4}}

$$\frac { \frac { 18 } { y + 4 } - 3 } { y - \frac { 12 } { y + 4 } }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{y+4}{y+4}.

$$\frac{\frac{18}{y+4}-\frac{3\left(y+4\right)}{y+4}}{y-\frac{12}{y+4}}$$

Since \frac{18}{y+4} and \frac{3\left(y+4\right)}{y+4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{18-3\left(y+4\right)}{y+4}}{y-\frac{12}{y+4}}$$

Do the multiplications in 18-3\left(y+4\right).

$$\frac{\frac{18-3y-12}{y+4}}{y-\frac{12}{y+4}}$$

Combine like terms in 18-3y-12.

$$\frac{\frac{6-3y}{y+4}}{y-\frac{12}{y+4}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{y+4}{y+4}.

$$\frac{\frac{6-3y}{y+4}}{\frac{y\left(y+4\right)}{y+4}-\frac{12}{y+4}}$$

Since \frac{y\left(y+4\right)}{y+4} and \frac{12}{y+4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{6-3y}{y+4}}{\frac{y\left(y+4\right)-12}{y+4}}$$

Do the multiplications in y\left(y+4\right)-12.

$$\frac{\frac{6-3y}{y+4}}{\frac{y^{2}+4y-12}{y+4}}$$

Divide \frac{6-3y}{y+4} by \frac{y^{2}+4y-12}{y+4} by multiplying \frac{6-3y}{y+4} by the reciprocal of \frac{y^{2}+4y-12}{y+4}.

$$\frac{\left(6-3y\right)\left(y+4\right)}{\left(y+4\right)\left(y^{2}+4y-12\right)}$$

Cancel out y+4 in both numerator and denominator.

$$\frac{-3y+6}{y^{2}+4y-12}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in 2-y.

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

Cancel out y-2 in both numerator and denominator.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{y+4}{y+4}.

$$\frac{\frac{18}{y+4}-\frac{3\left(y+4\right)}{y+4}}{y-\frac{12}{y+4}}$$

Since \frac{18}{y+4} and \frac{3\left(y+4\right)}{y+4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{18-3\left(y+4\right)}{y+4}}{y-\frac{12}{y+4}}$$

Do the multiplications in 18-3\left(y+4\right).

$$\frac{\frac{18-3y-12}{y+4}}{y-\frac{12}{y+4}}$$

Combine like terms in 18-3y-12.

$$\frac{\frac{6-3y}{y+4}}{y-\frac{12}{y+4}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{y+4}{y+4}.

$$\frac{\frac{6-3y}{y+4}}{\frac{y\left(y+4\right)}{y+4}-\frac{12}{y+4}}$$

Since \frac{y\left(y+4\right)}{y+4} and \frac{12}{y+4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{6-3y}{y+4}}{\frac{y\left(y+4\right)-12}{y+4}}$$

Do the multiplications in y\left(y+4\right)-12.

$$\frac{\frac{6-3y}{y+4}}{\frac{y^{2}+4y-12}{y+4}}$$

Divide \frac{6-3y}{y+4} by \frac{y^{2}+4y-12}{y+4} by multiplying \frac{6-3y}{y+4} by the reciprocal of \frac{y^{2}+4y-12}{y+4}.

$$\frac{\left(6-3y\right)\left(y+4\right)}{\left(y+4\right)\left(y^{2}+4y-12\right)}$$

Cancel out y+4 in both numerator and denominator.

$$\frac{-3y+6}{y^{2}+4y-12}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in 2-y.

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

Cancel out y-2 in both numerator and denominator.

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