Evaluate
\frac{x^{2}-11x+6}{x^{3}-8}
Expand
\frac{x^{2}-11x+6}{x^{3}-8}
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\frac{x^{2}-10x+4-\left(x-2\right)}{\left(x-2\right)\left(x^{2}+2x+4\right)}
Combine 2x and -12x to get -10x.
\frac{x^{2}-10x+4-x+2}{\left(x-2\right)\left(x^{2}+2x+4\right)}
To find the opposite of x-2, find the opposite of each term.
\frac{x^{2}-11x+4+2}{\left(x-2\right)\left(x^{2}+2x+4\right)}
Combine -10x and -x to get -11x.
\frac{x^{2}-11x+6}{\left(x-2\right)\left(x^{2}+2x+4\right)}
Add 4 and 2 to get 6.
\frac{x^{2}-11x+6}{x^{3}-8}
Use the distributive property to multiply x-2 by x^{2}+2x+4 and combine like terms.
\frac{x^{2}-10x+4-\left(x-2\right)}{\left(x-2\right)\left(x^{2}+2x+4\right)}
Combine 2x and -12x to get -10x.
\frac{x^{2}-10x+4-x+2}{\left(x-2\right)\left(x^{2}+2x+4\right)}
To find the opposite of x-2, find the opposite of each term.
\frac{x^{2}-11x+4+2}{\left(x-2\right)\left(x^{2}+2x+4\right)}
Combine -10x and -x to get -11x.
\frac{x^{2}-11x+6}{\left(x-2\right)\left(x^{2}+2x+4\right)}
Add 4 and 2 to get 6.
\frac{x^{2}-11x+6}{x^{3}-8}
Use the distributive property to multiply x-2 by x^{2}+2x+4 and combine like terms.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
y = 3x + 4
Arithmetic
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Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}