Solve 2x/x^2-12x+27*x^2-81/4x^3+36x^2

$$\frac { 2 x } { x ^ { 2 } - 12 x + 27 } \cdot \frac { x ^ { 2 } - 81 } { 4 x ^ { 3 } + 36 x ^ { 2 } }$$

Evaluate

$$\frac{1}{2x\left(x-3\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-81}{4x^{3}+36x^{2}}.

$$\frac{2x}{x^{2}-12x+27}\times \frac{\left(x-9\right)\left(x+9\right)}{4\left(x+9\right)x^{2}}$$

Cancel out x+9 in both numerator and denominator.

$$\frac{2x}{x^{2}-12x+27}\times \frac{x-9}{4x^{2}}$$

Multiply \frac{2x}{x^{2}-12x+27} times \frac{x-9}{4x^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2x\left(x-9\right)}{\left(x^{2}-12x+27\right)\times 4x^{2}}$$

Cancel out 2x in both numerator and denominator.

$$\frac{x-9}{2x\left(x^{2}-12x+27\right)}$$

Factor the expressions that are not already factored.

$$\frac{x-9}{2x\left(x-9\right)\left(x-3\right)}$$

Cancel out x-9 in both numerator and denominator.

$$\frac{1}{2x\left(x-3\right)}$$

Expand the expression.

$$\frac{1}{2x^{2}-6x}$$

Expand

$$\frac{1}{2x\left(x-3\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-81}{4x^{3}+36x^{2}}.

$$\frac{2x}{x^{2}-12x+27}\times \frac{\left(x-9\right)\left(x+9\right)}{4\left(x+9\right)x^{2}}$$

Cancel out x+9 in both numerator and denominator.

$$\frac{2x}{x^{2}-12x+27}\times \frac{x-9}{4x^{2}}$$

Multiply \frac{2x}{x^{2}-12x+27} times \frac{x-9}{4x^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2x\left(x-9\right)}{\left(x^{2}-12x+27\right)\times 4x^{2}}$$

Cancel out 2x in both numerator and denominator.

$$\frac{x-9}{2x\left(x^{2}-12x+27\right)}$$

Factor the expressions that are not already factored.

$$\frac{x-9}{2x\left(x-9\right)\left(x-3\right)}$$

Cancel out x-9 in both numerator and denominator.

$$\frac{1}{2x\left(x-3\right)}$$

Expand the expression.

$$\frac{1}{2x^{2}-6x}$$