Solve x/x^2-4/frac{x^2-x-12{x^3-8}}

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

Evaluate

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

Short Solution Steps

Rewrite x^{2} as xx. Cancel out x in both numerator and denominator.

$$\frac{\frac{1}{x}-4}{\frac{x^{2}-x-12}{x^{3}-8}}$$

Divide \frac{1}{x}-4 by \frac{x^{2}-x-12}{x^{3}-8} by multiplying \frac{1}{x}-4 by the reciprocal of \frac{x^{2}-x-12}{x^{3}-8}.

$$\frac{\left(\frac{1}{x}-4\right)\left(x^{3}-8\right)}{x^{2}-x-12}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x}{x}.

$$\frac{\left(\frac{1}{x}-\frac{4x}{x}\right)\left(x^{3}-8\right)}{x^{2}-x-12}$$

Since \frac{1}{x} and \frac{4x}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-4x}{x}\left(x^{3}-8\right)}{x^{2}-x-12}$$

Express \frac{1-4x}{x}\left(x^{3}-8\right) as a single fraction.

$$\frac{\frac{\left(1-4x\right)\left(x^{3}-8\right)}{x}}{x^{2}-x-12}$$

Express \frac{\frac{\left(1-4x\right)\left(x^{3}-8\right)}{x}}{x^{2}-x-12} as a single fraction.

$$\frac{\left(1-4x\right)\left(x^{3}-8\right)}{x\left(x^{2}-x-12\right)}$$

Use the distributive property to multiply 1-4x by x^{3}-8.

$$\frac{x^{3}-8-4x^{4}+32x}{x\left(x^{2}-x-12\right)}$$

Use the distributive property to multiply x by x^{2}-x-12.

$$\frac{x^{3}-8-4x^{4}+32x}{x^{3}-x^{2}-12x}$$

Expand

$$\frac{-4x^{4}+x^{3}+32x-8}{x\left(x^{2}-x-12\right)}$$

Short Solution Steps

Rewrite x^{2} as xx. Cancel out x in both numerator and denominator.

$$\frac{\frac{1}{x}-4}{\frac{x^{2}-x-12}{x^{3}-8}}$$

Divide \frac{1}{x}-4 by \frac{x^{2}-x-12}{x^{3}-8} by multiplying \frac{1}{x}-4 by the reciprocal of \frac{x^{2}-x-12}{x^{3}-8}.

$$\frac{\left(\frac{1}{x}-4\right)\left(x^{3}-8\right)}{x^{2}-x-12}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x}{x}.

$$\frac{\left(\frac{1}{x}-\frac{4x}{x}\right)\left(x^{3}-8\right)}{x^{2}-x-12}$$

Since \frac{1}{x} and \frac{4x}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-4x}{x}\left(x^{3}-8\right)}{x^{2}-x-12}$$

Express \frac{1-4x}{x}\left(x^{3}-8\right) as a single fraction.

$$\frac{\frac{\left(1-4x\right)\left(x^{3}-8\right)}{x}}{x^{2}-x-12}$$

Express \frac{\frac{\left(1-4x\right)\left(x^{3}-8\right)}{x}}{x^{2}-x-12} as a single fraction.

$$\frac{\left(1-4x\right)\left(x^{3}-8\right)}{x\left(x^{2}-x-12\right)}$$

Use the distributive property to multiply 1-4x by x^{3}-8.

$$\frac{x^{3}-8-4x^{4}+32x}{x\left(x^{2}-x-12\right)}$$

Use the distributive property to multiply x by x^{2}-x-12.

$$\frac{x^{3}-8-4x^{4}+32x}{x^{3}-x^{2}-12x}$$