Solve x+3/x^2-4/x^2-x-12/x^3-8

$$\frac { \frac { \frac { x + 3 } { x ^ { 2 } - 4 } } { x ^ { 2 } - x - 12 } } { x ^ { 3 } - 8 }$$

Evaluate

$$\frac{1}{\left(x-2\right)^{2}\left(x^{4}-8x^{2}-24x-32\right)}$$

Short Solution Steps

Express \frac{\frac{\frac{x+3}{x^{2}-4}}{x^{2}-x-12}}{x^{3}-8} as a single fraction.

$$\frac{\frac{x+3}{x^{2}-4}}{\left(x^{2}-x-12\right)\left(x^{3}-8\right)}$$

Express \frac{\frac{x+3}{x^{2}-4}}{\left(x^{2}-x-12\right)\left(x^{3}-8\right)} as a single fraction.

$$\frac{x+3}{\left(x^{2}-4\right)\left(x^{2}-x-12\right)\left(x^{3}-8\right)}$$

Factor the expressions that are not already factored.

$$\frac{x+3}{\left(x-4\right)\left(x+2\right)\left(x+3\right)\left(x-2\right)^{2}\left(x^{2}+2x+4\right)}$$

Cancel out x+3 in both numerator and denominator.

$$\frac{1}{\left(x-4\right)\left(x+2\right)\left(x-2\right)^{2}\left(x^{2}+2x+4\right)}$$

Expand the expression.

$$\frac{1}{x^{6}-4x^{5}-4x^{4}+8x^{3}+32x^{2}+32x-128}$$

Expand

$$\frac{1}{\left(x-4\right)\left(x^{2}-4\right)\left(x^{3}-8\right)}$$

Short Solution Steps

Express \frac{\frac{\frac{x+3}{x^{2}-4}}{x^{2}-x-12}}{x^{3}-8} as a single fraction.

$$\frac{\frac{x+3}{x^{2}-4}}{\left(x^{2}-x-12\right)\left(x^{3}-8\right)}$$

Express \frac{\frac{x+3}{x^{2}-4}}{\left(x^{2}-x-12\right)\left(x^{3}-8\right)} as a single fraction.

$$\frac{x+3}{\left(x^{2}-4\right)\left(x^{2}-x-12\right)\left(x^{3}-8\right)}$$

Factor the expressions that are not already factored.

$$\frac{x+3}{\left(x-4\right)\left(x+2\right)\left(x+3\right)\left(x-2\right)^{2}\left(x^{2}+2x+4\right)}$$

Cancel out x+3 in both numerator and denominator.

$$\frac{1}{\left(x-4\right)\left(x+2\right)\left(x-2\right)^{2}\left(x^{2}+2x+4\right)}$$

Expand the expression.

$$\frac{1}{x^{6}-4x^{5}-4x^{4}+8x^{3}+32x^{2}+32x-128}$$