Evaluate
\frac{-x^{3}-10x^{2}+x-10}{\left(x-1\right)\left(x^{2}+1\right)}
Expand
\frac{-x^{3}-10x^{2}+x-10}{\left(x-1\right)\left(x^{2}+1\right)}
Graph
Quiz
Polynomial
5 problems similar to:
\frac { 1 - x } { x ^ { 2 } + 1 } - \frac { x + 9 } { x - 1 } =
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\frac{\left(1-x\right)\left(x-1\right)}{\left(x-1\right)\left(x^{2}+1\right)}-\frac{\left(x+9\right)\left(x^{2}+1\right)}{\left(x-1\right)\left(x^{2}+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2}+1 and x-1 is \left(x-1\right)\left(x^{2}+1\right). Multiply \frac{1-x}{x^{2}+1} times \frac{x-1}{x-1}. Multiply \frac{x+9}{x-1} times \frac{x^{2}+1}{x^{2}+1}.
\frac{\left(1-x\right)\left(x-1\right)-\left(x+9\right)\left(x^{2}+1\right)}{\left(x-1\right)\left(x^{2}+1\right)}
Since \frac{\left(1-x\right)\left(x-1\right)}{\left(x-1\right)\left(x^{2}+1\right)} and \frac{\left(x+9\right)\left(x^{2}+1\right)}{\left(x-1\right)\left(x^{2}+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x-1-x^{2}+x-x^{3}-x-9x^{2}-9}{\left(x-1\right)\left(x^{2}+1\right)}
Do the multiplications in \left(1-x\right)\left(x-1\right)-\left(x+9\right)\left(x^{2}+1\right).
\frac{x-10-10x^{2}-x^{3}}{\left(x-1\right)\left(x^{2}+1\right)}
Combine like terms in x-1-x^{2}+x-x^{3}-x-9x^{2}-9.
\frac{x-10-10x^{2}-x^{3}}{x^{3}-x^{2}+x-1}
Expand \left(x-1\right)\left(x^{2}+1\right).
\frac{\left(1-x\right)\left(x-1\right)}{\left(x-1\right)\left(x^{2}+1\right)}-\frac{\left(x+9\right)\left(x^{2}+1\right)}{\left(x-1\right)\left(x^{2}+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2}+1 and x-1 is \left(x-1\right)\left(x^{2}+1\right). Multiply \frac{1-x}{x^{2}+1} times \frac{x-1}{x-1}. Multiply \frac{x+9}{x-1} times \frac{x^{2}+1}{x^{2}+1}.
\frac{\left(1-x\right)\left(x-1\right)-\left(x+9\right)\left(x^{2}+1\right)}{\left(x-1\right)\left(x^{2}+1\right)}
Since \frac{\left(1-x\right)\left(x-1\right)}{\left(x-1\right)\left(x^{2}+1\right)} and \frac{\left(x+9\right)\left(x^{2}+1\right)}{\left(x-1\right)\left(x^{2}+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x-1-x^{2}+x-x^{3}-x-9x^{2}-9}{\left(x-1\right)\left(x^{2}+1\right)}
Do the multiplications in \left(1-x\right)\left(x-1\right)-\left(x+9\right)\left(x^{2}+1\right).
\frac{x-10-10x^{2}-x^{3}}{\left(x-1\right)\left(x^{2}+1\right)}
Combine like terms in x-1-x^{2}+x-x^{3}-x-9x^{2}-9.
\frac{x-10-10x^{2}-x^{3}}{x^{3}-x^{2}+x-1}
Expand \left(x-1\right)\left(x^{2}+1\right).
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
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}