Solve 6y-24/9y^2-21y*63y-27y^2/4-y=

$$\frac { 6 y - 24 } { 9 y ^ { 2 } - 21 y } \cdot \frac { 63 y - 27 y ^ { 2 } } { 4 - y } =$$

Evaluate

$$18$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{6y-24}{9y^{2}-21y}.

$$\frac{6\left(y-4\right)}{3y\left(3y-7\right)}\times \frac{63y-27y^{2}}{4-y}$$

Cancel out 3 in both numerator and denominator.

$$\frac{2\left(y-4\right)}{y\left(3y-7\right)}\times \frac{63y-27y^{2}}{4-y}$$

Multiply \frac{2\left(y-4\right)}{y\left(3y-7\right)} times \frac{63y-27y^{2}}{4-y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(y-4\right)\left(63y-27y^{2}\right)}{y\left(3y-7\right)\left(4-y\right)}$$

Extract the negative sign in y-4.

$$\frac{-2\left(-y+4\right)\left(-27y^{2}+63y\right)}{y\left(3y-7\right)\left(-y+4\right)}$$

Cancel out -y+4 in both numerator and denominator.

$$\frac{-2\left(-27y^{2}+63y\right)}{y\left(3y-7\right)}$$

Factor the expressions that are not already factored.

$$\frac{-2\times 9y\left(-3y+7\right)}{y\left(3y-7\right)}$$

Extract the negative sign in 7-3y.

$$\frac{-2\left(-1\right)\times 9y\left(3y-7\right)}{y\left(3y-7\right)}$$

Cancel out y\left(3y-7\right) in both numerator and denominator.

$$-2\left(-1\right)\times 9$$

Multiply -2 and -1 to get 2.

$$2\times 9$$

Multiply 2 and 9 to get 18.

$$18$$

Factor

$$2\times 3^{2}$$