Solve 3y-6/4y+6div6y+24/8y+12

$$\frac { 3 y - 6 } { 4 y + 6 } \div \frac { 6 y + 24 } { 8 y + 12 }$$

Evaluate

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

Short Solution Steps

Divide \frac{3y-6}{4y+6} by \frac{6y+24}{8y+12} by multiplying \frac{3y-6}{4y+6} by the reciprocal of \frac{6y+24}{8y+12}.

$$\frac{\left(3y-6\right)\left(8y+12\right)}{\left(4y+6\right)\left(6y+24\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 2\times 2\times 3\left(2y+3\right) in both numerator and denominator.

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

Expand

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

Short Solution Steps

Divide \frac{3y-6}{4y+6} by \frac{6y+24}{8y+12} by multiplying \frac{3y-6}{4y+6} by the reciprocal of \frac{6y+24}{8y+12}.

$$\frac{\left(3y-6\right)\left(8y+12\right)}{\left(4y+6\right)\left(6y+24\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 2\times 2\times 3\left(2y+3\right) in both numerator and denominator.

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