Solve b^2-6b+9/4b^2-6b+9*27+8b^3/6-2b

$$\frac { b ^ { 2 } - 6 b + 9 } { 4 b ^ { 2 } - 6 b + 9 } \cdot \frac { 27 + 8 b ^ { 3 } } { 6 - 2 b }$$

Evaluate

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

Short Solution Steps

Multiply \frac{b^{2}-6b+9}{4b^{2}-6b+9} times \frac{27+8b^{3}}{6-2b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(b^{2}-6b+9\right)\left(27+8b^{3}\right)}{\left(4b^{2}-6b+9\right)\left(6-2b\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 4b^{2}-6b+9 in both numerator and denominator.

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

Expand the expression.

$$\frac{2b^{3}-9b^{2}+27}{-2b+6}$$

Expand

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

Short Solution Steps

Multiply \frac{b^{2}-6b+9}{4b^{2}-6b+9} times \frac{27+8b^{3}}{6-2b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(b^{2}-6b+9\right)\left(27+8b^{3}\right)}{\left(4b^{2}-6b+9\right)\left(6-2b\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 4b^{2}-6b+9 in both numerator and denominator.

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

Expand the expression.

$$\frac{2b^{3}-9b^{2}+27}{-2b+6}$$