Subtract. $$ \frac{x}{x^{2}-2 x-24}-\frac{x}{x^{2}-8 x+12} $$

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Calculate or simplify the expression $$ \frac{x}{x^{2}-2x-24}-\frac{x}{x^{2}-8x+12} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{x}{x^{2}-2x-24}-\frac{x}{x^{2}-8x+12}$$
- step1: Factor the expression:
  $$\frac{x}{\left(x+4\right)\left(x-6\right)}-\frac{x}{\left(x-2\right)\left(x-6\right)}$$
- step2: Reduce fractions to a common denominator:
  $$\frac{x\left(x-2\right)}{\left(x+4\right)\left(x-6\right)\left(x-2\right)}-\frac{x\left(x+4\right)}{\left(x-2\right)\left(x-6\right)\left(x+4\right)}$$
- step3: Rewrite the expression:
  $$\frac{x\left(x-2\right)}{\left(x+4\right)\left(x-6\right)\left(x-2\right)}-\frac{x\left(x+4\right)}{\left(x+4\right)\left(x-6\right)\left(x-2\right)}$$
- step4: Transform the expression:
  $$\frac{x\left(x-2\right)-x\left(x+4\right)}{\left(x+4\right)\left(x-6\right)\left(x-2\right)}$$
- step5: Multiply the terms:
  $$\frac{x^{2}-2x-x\left(x+4\right)}{\left(x+4\right)\left(x-6\right)\left(x-2\right)}$$
- step6: Multiply the terms:
  $$\frac{x^{2}-2x-\left(x^{2}+4x\right)}{\left(x+4\right)\left(x-6\right)\left(x-2\right)}$$
- step7: Subtract the terms:
  $$\frac{-6x}{\left(x+4\right)\left(x-6\right)\left(x-2\right)}$$
- step8: Rewrite the fraction:
  $$-\frac{6x}{\left(x+4\right)\left(x-6\right)\left(x-2\right)}$$
- step9: Calculate:
  $$-\frac{6x}{x^{3}-4x^{2}-20x+48}$$
The result of subtracting $$\frac{x}{x^{2}-2x-24}$$ from $$\frac{x}{x^{2}-8x+12}$$ is $$-\frac{6x}{x^{3}-4x^{2}-20x+48}$$.
The result of the subtraction is $$-\frac{6x}{x^{3}-4x^{2}-20x+48}$$.

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