Solve x+3/6a-6b*b-a/x^3+27=

$$\frac { x + 3 } { 6 a - 6 b } \cdot \frac { b - a } { x ^ { 3 } + 27 } =$$

Evaluate

$$-\frac{1}{6\left(x^{2}-3x+9\right)}$$

Short Solution Steps

Multiply \frac{x+3}{6a-6b} times \frac{b-a}{x^{3}+27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+3\right)\left(b-a\right)}{\left(6a-6b\right)\left(x^{3}+27\right)}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in b-a.

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

Cancel out \left(x+3\right)\left(a-b\right) in both numerator and denominator.

$$\frac{-1}{6\left(x^{2}-3x+9\right)}$$

Expand the expression.

$$\frac{-1}{6x^{2}-18x+54}$$

Expand

$$-\frac{1}{6\left(x^{2}-3x+9\right)}$$

Short Solution Steps

Multiply \frac{x+3}{6a-6b} times \frac{b-a}{x^{3}+27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+3\right)\left(b-a\right)}{\left(6a-6b\right)\left(x^{3}+27\right)}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in b-a.

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

Cancel out \left(x+3\right)\left(a-b\right) in both numerator and denominator.

$$\frac{-1}{6\left(x^{2}-3x+9\right)}$$

Expand the expression.

$$\frac{-1}{6x^{2}-18x+54}$$