Evaluate
\frac{8x^{2}-7x+9}{\left(3-x\right)\left(x^{2}+1\right)}
Expand
\frac{8x^{2}-7x+9}{\left(3-x\right)\left(x^{2}+1\right)}
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\frac{6\left(x^{2}+1\right)}{\left(-x+3\right)\left(x^{2}+1\right)}+\frac{\left(-2x+1\right)\left(-x+3\right)}{\left(-x+3\right)\left(x^{2}+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3-x and 1+x^{2} is \left(-x+3\right)\left(x^{2}+1\right). Multiply \frac{6}{3-x} times \frac{x^{2}+1}{x^{2}+1}. Multiply \frac{-2x+1}{1+x^{2}} times \frac{-x+3}{-x+3}.
\frac{6\left(x^{2}+1\right)+\left(-2x+1\right)\left(-x+3\right)}{\left(-x+3\right)\left(x^{2}+1\right)}
Since \frac{6\left(x^{2}+1\right)}{\left(-x+3\right)\left(x^{2}+1\right)} and \frac{\left(-2x+1\right)\left(-x+3\right)}{\left(-x+3\right)\left(x^{2}+1\right)} have the same denominator, add them by adding their numerators.
\frac{6x^{2}+6+2x^{2}-6x+3-x}{\left(-x+3\right)\left(x^{2}+1\right)}
Do the multiplications in 6\left(x^{2}+1\right)+\left(-2x+1\right)\left(-x+3\right).
\frac{8x^{2}+9-7x}{\left(-x+3\right)\left(x^{2}+1\right)}
Combine like terms in 6x^{2}+6+2x^{2}-6x+3-x.
\frac{8x^{2}+9-7x}{-x^{3}+3x^{2}-x+3}
Expand \left(-x+3\right)\left(x^{2}+1\right).
\frac{6\left(x^{2}+1\right)}{\left(-x+3\right)\left(x^{2}+1\right)}+\frac{\left(-2x+1\right)\left(-x+3\right)}{\left(-x+3\right)\left(x^{2}+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3-x and 1+x^{2} is \left(-x+3\right)\left(x^{2}+1\right). Multiply \frac{6}{3-x} times \frac{x^{2}+1}{x^{2}+1}. Multiply \frac{-2x+1}{1+x^{2}} times \frac{-x+3}{-x+3}.
\frac{6\left(x^{2}+1\right)+\left(-2x+1\right)\left(-x+3\right)}{\left(-x+3\right)\left(x^{2}+1\right)}
Since \frac{6\left(x^{2}+1\right)}{\left(-x+3\right)\left(x^{2}+1\right)} and \frac{\left(-2x+1\right)\left(-x+3\right)}{\left(-x+3\right)\left(x^{2}+1\right)} have the same denominator, add them by adding their numerators.
\frac{6x^{2}+6+2x^{2}-6x+3-x}{\left(-x+3\right)\left(x^{2}+1\right)}
Do the multiplications in 6\left(x^{2}+1\right)+\left(-2x+1\right)\left(-x+3\right).
\frac{8x^{2}+9-7x}{\left(-x+3\right)\left(x^{2}+1\right)}
Combine like terms in 6x^{2}+6+2x^{2}-6x+3-x.
\frac{8x^{2}+9-7x}{-x^{3}+3x^{2}-x+3}
Expand \left(-x+3\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}