Mister Exam
Least common denominator (z/x-z+x+z/z)/x/x^2-x*z^2
The solution
You have entered
[src]
/z z\
|- - z + x + -|
|x z|
|-------------|
\ x / 2
--------------- - x*z
2
x
$$- x z^{2} + \frac{\frac{1}{x} \left(\left(x + \left(- z + \frac{z}{x}\right)\right) + \frac{z}{z}\right)}{x^{2}}$$
((z/x - z + x + z/z)/x)/x^2 - x*z^2
General simplification
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5 2
z + x*(1 + x - z) - x *z
-------------------------
4
x
$$\frac{- x^{5} z^{2} + x \left(x - z + 1\right) + z}{x^{4}}$$
(z + x*(1 + x - z) - x^5*z^2)/x^4
Trigonometric part
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z
1 + x - z + -
x 2
------------- - x*z
3
x
$$- x z^{2} + \frac{x - z + 1 + \frac{z}{x}}{x^{3}}$$
(1 + x - z + z/x)/x^3 - x*z^2
Assemble expression
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/ 1\
1 + x + z*|-1 + -|
\ x/ 2
------------------ - x*z
3
x
$$- x z^{2} + \frac{x + z \left(-1 + \frac{1}{x}\right) + 1}{x^{3}}$$
z
1 + x - z + -
x 2
------------- - x*z
3
x
$$- x z^{2} + \frac{x - z + 1 + \frac{z}{x}}{x^{3}}$$
(1 + x - z + z/x)/x^3 - x*z^2
Common denominator
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2
x + z + x - x*z 2
---------------- - x*z
4
x
$$- x z^{2} + \frac{x^{2} - x z + x + z}{x^{4}}$$
(x + z + x^2 - x*z)/x^4 - x*z^2
Combinatorics
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/ 2 5 2\
-\-x - z - x + x*z + x *z /
-----------------------------
4
x
$$- \frac{x^{5} z^{2} - x^{2} + x z - x - z}{x^{4}}$$
-(-x - z - x^2 + x*z + x^5*z^2)/x^4
Rational denominator
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/ 2 \ 5 3
x*z + z*\z + x - x*z/ - x *z
------------------------------
4
x *z
$$\frac{- x^{5} z^{3} + x z + z \left(x^{2} - x z + z\right)}{x^{4} z}$$
(x*z + z*(z + x^2 - x*z) - x^5*z^3)/(x^4*z)
Powers
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z
1 + x - z + -
x 2
------------- - x*z
3
x
$$- x z^{2} + \frac{x - z + 1 + \frac{z}{x}}{x^{3}}$$
(1 + x - z + z/x)/x^3 - x*z^2
Combining rational expressions
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2 5 2
x + x + z*(1 - x) - x *z
--------------------------
4
x
$$\frac{- x^{5} z^{2} + x^{2} + x + z \left(1 - x\right)}{x^{4}}$$
(x + x^2 + z*(1 - x) - x^5*z^2)/x^4