Evaluate
\frac{x^{2}-6x+12}{x\left(x^{2}-36\right)}
Expand
\frac{x^{2}-6x+12}{x\left(x^{2}-36\right)}
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\frac{2x-2}{\left(x-6\right)\left(x+6\right)}-\frac{x-2}{x\left(x-6\right)}
Factor x^{2}-36. Factor x^{2}-6x.
\frac{\left(2x-2\right)x}{x\left(x-6\right)\left(x+6\right)}-\frac{\left(x-2\right)\left(x+6\right)}{x\left(x-6\right)\left(x+6\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-6\right)\left(x+6\right) and x\left(x-6\right) is x\left(x-6\right)\left(x+6\right). Multiply \frac{2x-2}{\left(x-6\right)\left(x+6\right)} times \frac{x}{x}. Multiply \frac{x-2}{x\left(x-6\right)} times \frac{x+6}{x+6}.
\frac{\left(2x-2\right)x-\left(x-2\right)\left(x+6\right)}{x\left(x-6\right)\left(x+6\right)}
Since \frac{\left(2x-2\right)x}{x\left(x-6\right)\left(x+6\right)} and \frac{\left(x-2\right)\left(x+6\right)}{x\left(x-6\right)\left(x+6\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{2x^{2}-2x-x^{2}-6x+2x+12}{x\left(x-6\right)\left(x+6\right)}
Do the multiplications in \left(2x-2\right)x-\left(x-2\right)\left(x+6\right).
\frac{x^{2}-6x+12}{x\left(x-6\right)\left(x+6\right)}
Combine like terms in 2x^{2}-2x-x^{2}-6x+2x+12.
\frac{x^{2}-6x+12}{x^{3}-36x}
Expand x\left(x-6\right)\left(x+6\right).
\frac{2x-2}{\left(x-6\right)\left(x+6\right)}-\frac{x-2}{x\left(x-6\right)}
Factor x^{2}-36. Factor x^{2}-6x.
\frac{\left(2x-2\right)x}{x\left(x-6\right)\left(x+6\right)}-\frac{\left(x-2\right)\left(x+6\right)}{x\left(x-6\right)\left(x+6\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-6\right)\left(x+6\right) and x\left(x-6\right) is x\left(x-6\right)\left(x+6\right). Multiply \frac{2x-2}{\left(x-6\right)\left(x+6\right)} times \frac{x}{x}. Multiply \frac{x-2}{x\left(x-6\right)} times \frac{x+6}{x+6}.
\frac{\left(2x-2\right)x-\left(x-2\right)\left(x+6\right)}{x\left(x-6\right)\left(x+6\right)}
Since \frac{\left(2x-2\right)x}{x\left(x-6\right)\left(x+6\right)} and \frac{\left(x-2\right)\left(x+6\right)}{x\left(x-6\right)\left(x+6\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{2x^{2}-2x-x^{2}-6x+2x+12}{x\left(x-6\right)\left(x+6\right)}
Do the multiplications in \left(2x-2\right)x-\left(x-2\right)\left(x+6\right).
\frac{x^{2}-6x+12}{x\left(x-6\right)\left(x+6\right)}
Combine like terms in 2x^{2}-2x-x^{2}-6x+2x+12.
\frac{x^{2}-6x+12}{x^{3}-36x}
Expand x\left(x-6\right)\left(x+6\right).
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