Mister Exam
Least common denominator (z/c+c/z)/z^2+c^2*z^15*c/6
The solution
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z c - + - 2 15 c z c *z *c ----- + -------- 2 6 z
$$\frac{c c^{2} z^{15}}{6} + \frac{\frac{c}{z} + \frac{z}{c}}{z^{2}}$$
(z/c + c/z)/z^2 + ((c^2*z^15)*c)/6
General simplification
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3 15 c 1 c *z -- + --- + ------ 3 c*z 6 z
$$\frac{c^{3} z^{15}}{6} + \frac{c}{z^{3}} + \frac{1}{c z}$$
c/z^3 + 1/(c*z) + c^3*z^15/6
Assemble expression
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c z - + - 3 15 z c c *z ----- + ------ 2 6 z
$$\frac{c^{3} z^{15}}{6} + \frac{\frac{c}{z} + \frac{z}{c}}{z^{2}}$$
(c/z + z/c)/z^2 + c^3*z^15/6
Trigonometric part
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c z - + - 3 15 z c c *z ----- + ------ 2 6 z
$$\frac{c^{3} z^{15}}{6} + \frac{\frac{c}{z} + \frac{z}{c}}{z^{2}}$$
(c/z + z/c)/z^2 + c^3*z^15/6
Powers
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c z - + - 3 15 z c c *z ----- + ------ 2 6 z
$$\frac{c^{3} z^{15}}{6} + \frac{\frac{c}{z} + \frac{z}{c}}{z^{2}}$$
(c/z + z/c)/z^2 + c^3*z^15/6
Rational denominator
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2 2 4 18
6*c + 6*z + c *z
--------------------
3
6*c*z
$$\frac{c^{4} z^{18} + 6 c^{2} + 6 z^{2}}{6 c z^{3}}$$
(6*c^2 + 6*z^2 + c^4*z^18)/(6*c*z^3)
Combinatorics
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2 2 4 18
6*c + 6*z + c *z
--------------------
3
6*c*z
$$\frac{c^{4} z^{18} + 6 c^{2} + 6 z^{2}}{6 c z^{3}}$$
(6*c^2 + 6*z^2 + c^4*z^18)/(6*c*z^3)
Numerical answer
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(c/z + z/c)/z^2 + 0.166666666666667*c^3*z^15
(c/z + z/c)/z^2 + 0.166666666666667*c^3*z^15
Combining rational expressions
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2 2 4 18
6*c + 6*z + c *z
--------------------
3
6*c*z
$$\frac{c^{4} z^{18} + 6 c^{2} + 6 z^{2}}{6 c z^{3}}$$
(6*c^2 + 6*z^2 + c^4*z^18)/(6*c*z^3)
Common denominator
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3 15 2 2
c *z c + z
------ + -------
6 3
c*z
$$\frac{c^{3} z^{15}}{6} + \frac{c^{2} + z^{2}}{c z^{3}}$$
c^3*z^15/6 + (c^2 + z^2)/(c*z^3)