Evaluate
\frac{x^{3}-2x-8}{x\left(x-2\right)^{2}}
Expand
\frac{x^{3}-2x-8}{x\left(x-2\right)^{2}}
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\frac{2x-8+\left(x+2\right)x\left(x-2\right)}{x\left(x-2\right)^{2}}
Since \frac{2x-8}{x\left(x-2\right)^{2}} and \frac{\left(x+2\right)x\left(x-2\right)}{x\left(x-2\right)^{2}} have the same denominator, add them by adding their numerators.
\frac{2x-8+x^{3}-2x^{2}+2x^{2}-4x}{x\left(x-2\right)^{2}}
Do the multiplications in 2x-8+\left(x+2\right)x\left(x-2\right).
\frac{-2x-8+x^{3}}{x\left(x-2\right)^{2}}
Combine like terms in 2x-8+x^{3}-2x^{2}+2x^{2}-4x.
\frac{-2x-8+x^{3}}{x^{3}-4x^{2}+4x}
Expand x\left(x-2\right)^{2}.
\frac{2x-8+\left(x+2\right)x\left(x-2\right)}{x\left(x-2\right)^{2}}
Since \frac{2x-8}{x\left(x-2\right)^{2}} and \frac{\left(x+2\right)x\left(x-2\right)}{x\left(x-2\right)^{2}} have the same denominator, add them by adding their numerators.
\frac{2x-8+x^{3}-2x^{2}+2x^{2}-4x}{x\left(x-2\right)^{2}}
Do the multiplications in 2x-8+\left(x+2\right)x\left(x-2\right).
\frac{-2x-8+x^{3}}{x\left(x-2\right)^{2}}
Combine like terms in 2x-8+x^{3}-2x^{2}+2x^{2}-4x.
\frac{-2x-8+x^{3}}{x^{3}-4x^{2}+4x}
Expand x\left(x-2\right)^{2}.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
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Limits
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