Mister Exam
Least common denominator ((x-x2+t)/2-x1+(abs((x-x2+t)/2-x1)))/2
The solution
You have entered
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x - x2 + t |x - x2 + t |
---------- - x1 + |---------- - x1|
2 | 2 |
-----------------------------------
2
$$\frac{\left(- x_{1} + \frac{t + \left(x - x_{2}\right)}{2}\right) + \left|{- x_{1} + \frac{t + \left(x - x_{2}\right)}{2}}\right|}{2}$$
((x - x2 + t)/2 - x1 + Abs((x - x2 + t)/2 - x1))/2
General simplification
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x1 x2 t x |t + x - x2 - 2*x1| - -- - -- + - + - + ------------------- 2 4 4 4 4
$$\frac{t}{4} + \frac{x}{4} - \frac{x_{1}}{2} - \frac{x_{2}}{4} + \frac{\left|{t + x - 2 x_{1} - x_{2}}\right|}{4}$$
-x1/2 - x2/4 + t/4 + x/4 + |t + x - x2 - 2*x1|/4
Combining rational expressions
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t + x - x2 - 2*x1 + |t + x - x2 - 2*x1|
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4
$$\frac{t + x - 2 x_{1} - x_{2} + \left|{t + x - 2 x_{1} - x_{2}}\right|}{4}$$
(t + x - x2 - 2*x1 + |t + x - x2 - 2*x1|)/4
Combinatorics
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|t x x2|
|- + - - x1 - --|
|2 2 2 | x1 x2 t x
----------------- - -- - -- + - + -
2 2 4 4 4
$$\frac{t}{4} + \frac{x}{4} - \frac{x_{1}}{2} - \frac{x_{2}}{4} + \frac{\left|{\frac{t}{2} + \frac{x}{2} - x_{1} - \frac{x_{2}}{2}}\right|}{2}$$
|t/2 + x/2 - x1 - x2/2|/2 - x1/2 - x2/4 + t/4 + x/4
Common denominator
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|t x x2|
|- + - - x1 - --|
|2 2 2 | x1 x2 t x
----------------- - -- - -- + - + -
2 2 4 4 4
$$\frac{t}{4} + \frac{x}{4} - \frac{x_{1}}{2} - \frac{x_{2}}{4} + \frac{\left|{\frac{t}{2} + \frac{x}{2} - x_{1} - \frac{x_{2}}{2}}\right|}{2}$$
|t/2 + x/2 - x1 - x2/2|/2 - x1/2 - x2/4 + t/4 + x/4
Trigonometric part
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|t x x2|
|- + - - x1 - --|
|2 2 2 | x1 x2 t x
----------------- - -- - -- + - + -
2 2 4 4 4
$$\frac{t}{4} + \frac{x}{4} - \frac{x_{1}}{2} - \frac{x_{2}}{4} + \frac{\left|{\frac{t}{2} + \frac{x}{2} - x_{1} - \frac{x_{2}}{2}}\right|}{2}$$
|t/2 + x/2 - x1 - x2/2|/2 - x1/2 - x2/4 + t/4 + x/4
Powers
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|t x x2|
|- + - - x1 - --|
|2 2 2 | x1 x2 t x
----------------- - -- - -- + - + -
2 2 4 4 4
$$\frac{t}{4} + \frac{x}{4} - \frac{x_{1}}{2} - \frac{x_{2}}{4} + \frac{\left|{\frac{t}{2} + \frac{x}{2} - x_{1} - \frac{x_{2}}{2}}\right|}{2}$$
|t/2 + x/2 - x1 - x2/2|/2 - x1/2 - x2/4 + t/4 + x/4
Numerical answer
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0.25*t + 0.25*x + 0.5*Abs((x - x2 + t)/2 - x1) - 0.25*x2 - 0.5*x1
0.25*t + 0.25*x + 0.5*Abs((x - x2 + t)/2 - x1) - 0.25*x2 - 0.5*x1
Rational denominator
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|t x x2|
t + x - x2 - 2*x1 + 2*|- + - - x1 - --|
|2 2 2 |
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4
$$\frac{t + x - 2 x_{1} - x_{2} + 2 \left|{\frac{t}{2} + \frac{x}{2} - x_{1} - \frac{x_{2}}{2}}\right|}{4}$$
(t + x - x2 - 2*x1 + 2*|t/2 + x/2 - x1 - x2/2|)/4
Assemble expression
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|x - x2 + t |
|---------- - x1|
| 2 | x1 x2 t x
----------------- - -- - -- + - + -
2 2 4 4 4
$$\frac{t}{4} + \frac{x}{4} - \frac{x_{1}}{2} - \frac{x_{2}}{4} + \frac{\left|{- x_{1} + \frac{t + \left(x - x_{2}\right)}{2}}\right|}{2}$$
Abs((x - x2 + t)/2 - x1)/2 - x1/2 - x2/4 + t/4 + x/4