Mister Exam
Least common denominator (x^2-8*x/9+493/1000)*(x-x^2/2)/3
The solution
You have entered
[src]
/ 2\
/ 2 8*x 493 \ | x |
|x - --- + ----|*|x - --|
\ 9 1000/ \ 2 /
--------------------------
3
$$\frac{\left(- \frac{x^{2}}{2} + x\right) \left(\left(x^{2} - \frac{8 x}{9}\right) + \frac{493}{1000}\right)}{3}$$
((x^2 - 8*x/9 + 493/1000)*(x - x^2/2))/3
General simplification
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/ 2\
-x*(-2 + x)*\4437 - 8000*x + 9000*x /
--------------------------------------
54000
$$- \frac{x \left(x - 2\right) \left(9000 x^{2} - 8000 x + 4437\right)}{54000}$$
-x*(-2 + x)*(4437 - 8000*x + 9000*x^2)/54000
Fraction decomposition
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-20437*x^2/54000 - x^4/6 + 13*x^3/27 + 493*x/3000
$$- \frac{x^{4}}{6} + \frac{13 x^{3}}{27} - \frac{20437 x^{2}}{54000} + \frac{493 x}{3000}$$
2 4 3 20437*x x 13*x 493*x - -------- - -- + ----- + ----- 54000 6 27 3000
Factorization
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/ ________\ / ________\
| 4 I*\/ 239330 | | 4 I*\/ 239330 |
x*(x - 2)*|x + - - + ------------|*|x + - - - ------------|
\ 9 900 / \ 9 900 /
$$x \left(x - 2\right) \left(x + \left(- \frac{4}{9} + \frac{\sqrt{239330} i}{900}\right)\right) \left(x + \left(- \frac{4}{9} - \frac{\sqrt{239330} i}{900}\right)\right)$$
((x*(x - 2))*(x - 4/9 + i*sqrt(239330)/900))*(x - 4/9 - i*sqrt(239330)/900)
Numerical answer
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0.333333333333333*(x - 0.5*x^2)*(0.493 + x^2 - 0.888888888888889*x)
0.333333333333333*(x - 0.5*x^2)*(0.493 + x^2 - 0.888888888888889*x)
Common denominator
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2 4 3 20437*x x 13*x 493*x - -------- - -- + ----- + ----- 54000 6 27 3000
$$- \frac{x^{4}}{6} + \frac{13 x^{3}}{27} - \frac{20437 x^{2}}{54000} + \frac{493 x}{3000}$$
-20437*x^2/54000 - x^4/6 + 13*x^3/27 + 493*x/3000
Combining rational expressions
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x*(2 - x)*(4437 + 1000*x*(-8 + 9*x))
------------------------------------
54000
$$\frac{x \left(2 - x\right) \left(1000 x \left(9 x - 8\right) + 4437\right)}{54000}$$
x*(2 - x)*(4437 + 1000*x*(-8 + 9*x))/54000
Trigonometric part
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/ 2\
| x | /493 2 8*x\
|x - --|*|---- + x - ---|
\ 2 / \1000 9 /
--------------------------
3
$$\frac{\left(- \frac{x^{2}}{2} + x\right) \left(x^{2} - \frac{8 x}{9} + \frac{493}{1000}\right)}{3}$$
(x - x^2/2)*(493/1000 + x^2 - 8*x/9)/3
Combinatorics
[src]
/ 2\
-x*(-2 + x)*\4437 - 8000*x + 9000*x /
--------------------------------------
54000
$$- \frac{x \left(x - 2\right) \left(9000 x^{2} - 8000 x + 4437\right)}{54000}$$
-x*(-2 + x)*(4437 - 8000*x + 9000*x^2)/54000
Assemble expression
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/ 2\
| x | /493 2 8*x\
|x - --|*|---- + x - ---|
\ 2 / \1000 9 /
--------------------------
3
$$\frac{\left(- \frac{x^{2}}{2} + x\right) \left(x^{2} - \frac{8 x}{9} + \frac{493}{1000}\right)}{3}$$
(x - x^2/2)*(493/1000 + x^2 - 8*x/9)/3
Powers
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/ 2\
| x | /493 2 8*x\
|x - --|*|---- + x - ---|
\ 2 / \1000 9 /
--------------------------
3
$$\frac{\left(- \frac{x^{2}}{2} + x\right) \left(x^{2} - \frac{8 x}{9} + \frac{493}{1000}\right)}{3}$$
(x - x^2/2)*(493/1000 + x^2 - 8*x/9)/3
Rational denominator
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/ 2 \ / 2\
\- x + 2*x/*\4437 - 8000*x + 9000*x /
--------------------------------------
54000
$$\frac{\left(- x^{2} + 2 x\right) \left(9000 x^{2} - 8000 x + 4437\right)}{54000}$$
(-x^2 + 2*x)*(4437 - 8000*x + 9000*x^2)/54000