Mister Exam
Least common denominator x^4/4+5*x^2/2-4*x
The solution
You have entered
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4 2 x 5*x -- + ---- - 4*x 4 2
$$- 4 x + \left(\frac{x^{4}}{4} + \frac{5 x^{2}}{2}\right)$$
x^4/4 + (5*x^2)/2 - 4*x
Fraction decomposition
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-4*x + x^4/4 + 5*x^2/2
$$\frac{x^{4}}{4} + \frac{5 x^{2}}{2} - 4 x$$
4 2
x 5*x
-4*x + -- + ----
4 2
General simplification
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/ 3 \
x*\-16 + x + 10*x/
-------------------
4
$$\frac{x \left(x^{3} + 10 x - 16\right)}{4}$$
x*(-16 + x^3 + 10*x)/4
Factorization
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$$x \left(x + \left(\frac{10}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8 + \frac{2 \sqrt{2046}}{9}}} - \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8 + \frac{2 \sqrt{2046}}{9}}\right)\right) \left(x + \left(- \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8 + \frac{2 \sqrt{2046}}{9}} + \frac{10}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{8 + \frac{2 \sqrt{2046}}{9}}}\right)\right) \left(x + \left(- \sqrt[3]{8 + \frac{2 \sqrt{2046}}{9}} + \frac{10}{3 \sqrt[3]{8 + \frac{2 \sqrt{2046}}{9}}}\right)\right)$$
((x*(x - (8 + 2*sqrt(2046)/9)^(1/3)*(-1/2 - i*sqrt(3)/2) + 10/(3*(8 + 2*sqrt(2046)/9)^(1/3)*(-1/2 - i*sqrt(3)/2))))*(x - (8 + 2*sqrt(2046)/9)^(1/3)*(-1/2 + i*sqrt(3)/2) + 10/(3*(8 + 2*sqrt(2046)/9)^(1/3)*(-1/2 + i*sqrt(3)/2))))*(x - (8 + 2*sqrt(2046)/9)^(1/3) + 10/(3*(8 + 2*sqrt(2046)/9)^(1/3)))
Trigonometric part
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4 2
x 5*x
-4*x + -- + ----
4 2
$$\frac{x^{4}}{4} + \frac{5 x^{2}}{2} - 4 x$$
-4*x + x^4/4 + 5*x^2/2
Rational denominator
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4 2
-32*x + 2*x + 20*x
--------------------
8
$$\frac{2 x^{4} + 20 x^{2} - 32 x}{8}$$
(-32*x + 2*x^4 + 20*x^2)/8
Common denominator
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4 2
x 5*x
-4*x + -- + ----
4 2
$$\frac{x^{4}}{4} + \frac{5 x^{2}}{2} - 4 x$$
-4*x + x^4/4 + 5*x^2/2
Combining rational expressions
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/ / 2\\
x*\-16 + x*\10 + x //
---------------------
4
$$\frac{x \left(x \left(x^{2} + 10\right) - 16\right)}{4}$$
x*(-16 + x*(10 + x^2))/4
Assemble expression
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4 2
x 5*x
-4*x + -- + ----
4 2
$$\frac{x^{4}}{4} + \frac{5 x^{2}}{2} - 4 x$$
-4*x + x^4/4 + 5*x^2/2
Powers
[src]
4 2
x 5*x
-4*x + -- + ----
4 2
$$\frac{x^{4}}{4} + \frac{5 x^{2}}{2} - 4 x$$
-4*x + x^4/4 + 5*x^2/2
Combinatorics
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/ 3 \
x*\-16 + x + 10*x/
-------------------
4
$$\frac{x \left(x^{3} + 10 x - 16\right)}{4}$$
x*(-16 + x^3 + 10*x)/4