Evaluate
\frac{x^{4}-x^{3}-20x^{2}+3x-117}{r\left(-7r^{3}+16r^{2}-22\right)}
Expand
\frac{x^{4}-x^{3}-20x^{2}+3x-117}{-7r^{4}+16r^{3}-22r}
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\frac{x^{4}-x^{3}-20x^{2}+3x-117}{-2r^{4}+12r^{3}-12r+4r^{3}-\left(5r^{4}+10r\right)}
Use the distributive property to multiply -2r by r^{3}-6r^{2}+6.
\frac{x^{4}-x^{3}-20x^{2}+3x-117}{-2r^{4}+16r^{3}-12r-\left(5r^{4}+10r\right)}
Combine 12r^{3} and 4r^{3} to get 16r^{3}.
\frac{x^{4}-x^{3}-20x^{2}+3x-117}{-2r^{4}+16r^{3}-12r-5r^{4}-10r}
To find the opposite of 5r^{4}+10r, find the opposite of each term.
\frac{x^{4}-x^{3}-20x^{2}+3x-117}{-7r^{4}+16r^{3}-12r-10r}
Combine -2r^{4} and -5r^{4} to get -7r^{4}.
\frac{x^{4}-x^{3}-20x^{2}+3x-117}{-7r^{4}+16r^{3}-22r}
Combine -12r and -10r to get -22r.
\frac{x^{4}-x^{3}-20x^{2}+3x-117}{-2r^{4}+12r^{3}-12r+4r^{3}-\left(5r^{4}+10r\right)}
Use the distributive property to multiply -2r by r^{3}-6r^{2}+6.
\frac{x^{4}-x^{3}-20x^{2}+3x-117}{-2r^{4}+16r^{3}-12r-\left(5r^{4}+10r\right)}
Combine 12r^{3} and 4r^{3} to get 16r^{3}.
\frac{x^{4}-x^{3}-20x^{2}+3x-117}{-2r^{4}+16r^{3}-12r-5r^{4}-10r}
To find the opposite of 5r^{4}+10r, find the opposite of each term.
\frac{x^{4}-x^{3}-20x^{2}+3x-117}{-7r^{4}+16r^{3}-12r-10r}
Combine -2r^{4} and -5r^{4} to get -7r^{4}.
\frac{x^{4}-x^{3}-20x^{2}+3x-117}{-7r^{4}+16r^{3}-22r}
Combine -12r and -10r to get -22r.
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Simultaneous equation
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Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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