Evaluate
-x+2+\frac{5}{2x}+\frac{7}{2x^{2}}+\frac{1}{2x^{3}}
Expand
-x+2+\frac{5}{2x}+\frac{7}{2x^{2}}+\frac{1}{2x^{3}}
Graph
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\frac{-2\left(x-\left(-\frac{1}{2}\sqrt{11}+\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{11}+\frac{3}{2}\right)\right)\left(x^{2}+x+1\right)}{2x^{3}}
Factor the expressions that are not already factored.
\frac{-\left(x-\left(-\frac{1}{2}\sqrt{11}+\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{11}+\frac{3}{2}\right)\right)\left(x^{2}+x+1\right)}{x^{3}}
Cancel out 2 in both numerator and denominator.
\frac{-x^{4}+2x^{3}+\frac{5}{2}x^{2}+\frac{7}{2}x+\frac{1}{2}}{x^{3}}
Expand the expression.
\frac{-2\left(x-\left(-\frac{1}{2}\sqrt{11}+\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{11}+\frac{3}{2}\right)\right)\left(x^{2}+x+1\right)}{2x^{3}}
Factor the expressions that are not already factored.
\frac{-\left(x-\left(-\frac{1}{2}\sqrt{11}+\frac{3}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{11}+\frac{3}{2}\right)\right)\left(x^{2}+x+1\right)}{x^{3}}
Cancel out 2 in both numerator and denominator.
\frac{-x^{4}+2x^{3}+\frac{5}{2}x^{2}+\frac{7}{2}x+\frac{1}{2}}{x^{3}}
Expand the expression.
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}