Evaluate
\frac{5-2x}{x^{3}-1}
Expand
\frac{5-2x}{x^{3}-1}
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\frac{2\left(x^{2}+x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)}+\frac{\left(x-3\right)\left(x-1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)}-\frac{3x^{2}}{x^{3}-1}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and x^{2}+x+1 is \left(x-1\right)\left(x^{2}+x+1\right). Multiply \frac{2}{x-1} times \frac{x^{2}+x+1}{x^{2}+x+1}. Multiply \frac{x-3}{x^{2}+x+1} times \frac{x-1}{x-1}.
\frac{2\left(x^{2}+x+1\right)+\left(x-3\right)\left(x-1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)}-\frac{3x^{2}}{x^{3}-1}
Since \frac{2\left(x^{2}+x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)} and \frac{\left(x-3\right)\left(x-1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)} have the same denominator, add them by adding their numerators.
\frac{2x^{2}+2x+2+x^{2}-x-3x+3}{\left(x-1\right)\left(x^{2}+x+1\right)}-\frac{3x^{2}}{x^{3}-1}
Do the multiplications in 2\left(x^{2}+x+1\right)+\left(x-3\right)\left(x-1\right).
\frac{3x^{2}-2x+5}{\left(x-1\right)\left(x^{2}+x+1\right)}-\frac{3x^{2}}{x^{3}-1}
Combine like terms in 2x^{2}+2x+2+x^{2}-x-3x+3.
\frac{3x^{2}-2x+5}{\left(x-1\right)\left(x^{2}+x+1\right)}-\frac{3x^{2}}{\left(x-1\right)\left(x^{2}+x+1\right)}
Factor x^{3}-1.
\frac{3x^{2}-2x+5-3x^{2}}{\left(x-1\right)\left(x^{2}+x+1\right)}
Since \frac{3x^{2}-2x+5}{\left(x-1\right)\left(x^{2}+x+1\right)} and \frac{3x^{2}}{\left(x-1\right)\left(x^{2}+x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{-2x+5}{\left(x-1\right)\left(x^{2}+x+1\right)}
Combine like terms in 3x^{2}-2x+5-3x^{2}.
\frac{-2x+5}{x^{3}-1}
Expand \left(x-1\right)\left(x^{2}+x+1\right).
\frac{2\left(x^{2}+x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)}+\frac{\left(x-3\right)\left(x-1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)}-\frac{3x^{2}}{x^{3}-1}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and x^{2}+x+1 is \left(x-1\right)\left(x^{2}+x+1\right). Multiply \frac{2}{x-1} times \frac{x^{2}+x+1}{x^{2}+x+1}. Multiply \frac{x-3}{x^{2}+x+1} times \frac{x-1}{x-1}.
\frac{2\left(x^{2}+x+1\right)+\left(x-3\right)\left(x-1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)}-\frac{3x^{2}}{x^{3}-1}
Since \frac{2\left(x^{2}+x+1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)} and \frac{\left(x-3\right)\left(x-1\right)}{\left(x-1\right)\left(x^{2}+x+1\right)} have the same denominator, add them by adding their numerators.
\frac{2x^{2}+2x+2+x^{2}-x-3x+3}{\left(x-1\right)\left(x^{2}+x+1\right)}-\frac{3x^{2}}{x^{3}-1}
Do the multiplications in 2\left(x^{2}+x+1\right)+\left(x-3\right)\left(x-1\right).
\frac{3x^{2}-2x+5}{\left(x-1\right)\left(x^{2}+x+1\right)}-\frac{3x^{2}}{x^{3}-1}
Combine like terms in 2x^{2}+2x+2+x^{2}-x-3x+3.
\frac{3x^{2}-2x+5}{\left(x-1\right)\left(x^{2}+x+1\right)}-\frac{3x^{2}}{\left(x-1\right)\left(x^{2}+x+1\right)}
Factor x^{3}-1.
\frac{3x^{2}-2x+5-3x^{2}}{\left(x-1\right)\left(x^{2}+x+1\right)}
Since \frac{3x^{2}-2x+5}{\left(x-1\right)\left(x^{2}+x+1\right)} and \frac{3x^{2}}{\left(x-1\right)\left(x^{2}+x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{-2x+5}{\left(x-1\right)\left(x^{2}+x+1\right)}
Combine like terms in 3x^{2}-2x+5-3x^{2}.
\frac{-2x+5}{x^{3}-1}
Expand \left(x-1\right)\left(x^{2}+x+1\right).
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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}