Mister Exam
How do you x/(x^3-3x+2) in partial fractions?
The solution
You have entered
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x ------------ 3 x - 3*x + 2
$$\frac{x}{\left(x^{3} - 3 x\right) + 2}$$
x/(x^3 - 3*x + 2)
General simplification
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x
------------
3
2 + x - 3*x
$$\frac{x}{x^{3} - 3 x + 2}$$
x/(2 + x^3 - 3*x)
Fraction decomposition
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-2/(9*(2 + x)) + 1/(3*(-1 + x)^2) + 2/(9*(-1 + x))
$$- \frac{2}{9 \left(x + 2\right)} + \frac{2}{9 \left(x - 1\right)} + \frac{1}{3 \left(x - 1\right)^{2}}$$
2 1 2
- --------- + ----------- + ----------
9*(2 + x) 2 9*(-1 + x)
3*(-1 + x)
Combinatorics
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x
-----------------
2
(-1 + x) *(2 + x)
$$\frac{x}{\left(x - 1\right)^{2} \left(x + 2\right)}$$
x/((-1 + x)^2*(2 + x))
Trigonometric part
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x
------------
3
2 + x - 3*x
$$\frac{x}{x^{3} - 3 x + 2}$$
x/(2 + x^3 - 3*x)
Combining rational expressions
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x
---------------
/ 2\
2 + x*\-3 + x /
$$\frac{x}{x \left(x^{2} - 3\right) + 2}$$
x/(2 + x*(-3 + x^2))
Assemble expression
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x
------------
3
2 + x - 3*x
$$\frac{x}{x^{3} - 3 x + 2}$$
x/(2 + x^3 - 3*x)
Common denominator
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x
------------
3
2 + x - 3*x
$$\frac{x}{x^{3} - 3 x + 2}$$
x/(2 + x^3 - 3*x)
Rational denominator
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x
------------
3
2 + x - 3*x
$$\frac{x}{x^{3} - 3 x + 2}$$
x/(2 + x^3 - 3*x)