Mister Exam
Least common denominator x*((x-1)^2/x^2)*(2/x-2*(x-1)/x^2)/(x-1)
The solution
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2
(x - 1) /2 2*(x - 1)\
x*--------*|- - ---------|
2 |x 2 |
x \ x /
--------------------------
x - 1
$$\frac{x \frac{\left(x - 1\right)^{2}}{x^{2}} \left(- \frac{2 \left(x - 1\right)}{x^{2}} + \frac{2}{x}\right)}{x - 1}$$
((x*((x - 1)^2/x^2))*(2/x - 2*(x - 1)/x^2))/(x - 1)
General simplification
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2*(-1 + x)
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3
x
$$\frac{2 \left(x - 1\right)}{x^{3}}$$
2*(-1 + x)/x^3
Fraction decomposition
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-2/x^3 + 2/x^2
$$\frac{2}{x^{2}} - \frac{2}{x^{3}}$$
2 2 - -- + -- 3 2 x x
Numerical answer
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(-1.0 + x)*(2.0/x - (-2.0 + 2.0*x)/x^2)/x
(-1.0 + x)*(2.0/x - (-2.0 + 2.0*x)/x^2)/x
Trigonometric part
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/2 -2 + 2*x\
(-1 + x)*|- - --------|
|x 2 |
\ x /
-----------------------
x
$$\frac{\left(\frac{2}{x} - \frac{2 x - 2}{x^{2}}\right) \left(x - 1\right)}{x}$$
(-1 + x)*(2/x - (-2 + 2*x)/x^2)/x
Combining rational expressions
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2*(-1 + x)
----------
3
x
$$\frac{2 \left(x - 1\right)}{x^{3}}$$
2*(-1 + x)/x^3
Rational denominator
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/ 2 \
(-1 + x)*\2*x + x*(2 - 2*x)/
-----------------------------
4
x
$$\frac{\left(x - 1\right) \left(2 x^{2} + x \left(2 - 2 x\right)\right)}{x^{4}}$$
(-1 + x)*(2*x^2 + x*(2 - 2*x))/x^4
Powers
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/2 -2 + 2*x\
(-1 + x)*|- - --------|
|x 2 |
\ x /
-----------------------
x
$$\frac{\left(\frac{2}{x} - \frac{2 x - 2}{x^{2}}\right) \left(x - 1\right)}{x}$$
/2 2 - 2*x\
(-1 + x)*|- + -------|
|x 2 |
\ x /
----------------------
x
$$\frac{\left(\frac{2}{x} + \frac{2 - 2 x}{x^{2}}\right) \left(x - 1\right)}{x}$$
(-1 + x)*(2/x + (2 - 2*x)/x^2)/x
Assemble expression
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/2 -2 + 2*x\
(-1 + x)*|- - --------|
|x 2 |
\ x /
-----------------------
x
$$\frac{\left(\frac{2}{x} - \frac{2 x - 2}{x^{2}}\right) \left(x - 1\right)}{x}$$
(-1 + x)*(2/x - (-2 + 2*x)/x^2)/x