Solve 3k^2-18b+27/3y-12:9-b^2/3y-12+by-4b=

$$\frac { 3 k ^ { 2 } - 18 b + 27 } { 3 y - 12 } : \frac { 9 - b ^ { 2 } } { 3 y - 12 + b y - 4 b } =$$

Evaluate

$$-\frac{9+k^{2}-6b}{b-3}$$

$$y\neq 4\text{ and }|b|\neq 3$$

Short Solution Steps

Divide \frac{3k^{2}-18b+27}{3y-12} by \frac{9-b^{2}}{3y-12+by-4b} by multiplying \frac{3k^{2}-18b+27}{3y-12} by the reciprocal of \frac{9-b^{2}}{3y-12+by-4b}.

$$\frac{\left(3k^{2}-18b+27\right)\left(3y-12+by-4b\right)}{\left(3y-12\right)\left(9-b^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{3\left(y-4\right)\left(b+3\right)\left(k^{2}-6b+9\right)}{3\left(b-3\right)\left(y-4\right)\left(-b-3\right)}$$

Extract the negative sign in 3+b.

$$\frac{-3\left(y-4\right)\left(-b-3\right)\left(k^{2}-6b+9\right)}{3\left(b-3\right)\left(y-4\right)\left(-b-3\right)}$$

Cancel out 3\left(y-4\right)\left(-b-3\right) in both numerator and denominator.

$$\frac{-\left(-6b+k^{2}+9\right)}{b-3}$$

Expand the expression.

$$\frac{6b-k^{2}-9}{b-3}$$

Expand

$$-\frac{6b-k^{2}-9}{3-b}$$

$$y\neq 4\text{ and }|b|\neq 3$$

Short Solution Steps

Divide \frac{3k^{2}-18b+27}{3y-12} by \frac{9-b^{2}}{3y-12+by-4b} by multiplying \frac{3k^{2}-18b+27}{3y-12} by the reciprocal of \frac{9-b^{2}}{3y-12+by-4b}.

$$\frac{\left(3k^{2}-18b+27\right)\left(3y-12+by-4b\right)}{\left(3y-12\right)\left(9-b^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{3\left(y-4\right)\left(b+3\right)\left(k^{2}-6b+9\right)}{3\left(b-3\right)\left(y-4\right)\left(-b-3\right)}$$

Extract the negative sign in 3+b.

$$\frac{-3\left(y-4\right)\left(-b-3\right)\left(k^{2}-6b+9\right)}{3\left(b-3\right)\left(y-4\right)\left(-b-3\right)}$$

Cancel out 3\left(y-4\right)\left(-b-3\right) in both numerator and denominator.

$$\frac{-\left(-6b+k^{2}+9\right)}{b-3}$$

Expand the expression.

$$\frac{6b-k^{2}-9}{b-3}$$