Mister Exam
Least common denominator x/y2+x*y+x-y/x2-x*y
The solution
You have entered
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x y -- + x*y + x - -- - x*y y2 x2
$$- x y + \left(\left(x + \left(x y + \frac{x}{y_{2}}\right)\right) - \frac{y}{x_{2}}\right)$$
x/y2 + x*y + x - y/x2 - x*y
General simplification
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x y
x + -- - --
y2 x2
$$x + \frac{x}{y_{2}} - \frac{y}{x_{2}}$$
x + x/y2 - y/x2
Combining rational expressions
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-y*y2 + x*x2*(1 + y2 + y*y2) - x*x2*y*y2
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x2*y2
$$\frac{- x x_{2} y y_{2} + x x_{2} \left(y y_{2} + y_{2} + 1\right) - y y_{2}}{x_{2} y_{2}}$$
(-y*y2 + x*x2*(1 + y2 + y*y2) - x*x2*y*y2)/(x2*y2)
Assemble expression
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/ 1 \ y x*|1 + --| - -- \ y2/ x2
$$x \left(1 + \frac{1}{y_{2}}\right) - \frac{y}{x_{2}}$$
x y
x + -- - --
y2 x2
$$x + \frac{x}{y_{2}} - \frac{y}{x_{2}}$$
x + x/y2 - y/x2
Trigonometric part
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x y
x + -- - --
y2 x2
$$x + \frac{x}{y_{2}} - \frac{y}{x_{2}}$$
x + x/y2 - y/x2
Rational denominator
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x2*(x + x*y2 + x*y*y2) - y*y2 - x*x2*y*y2
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x2*y2
$$\frac{- x x_{2} y y_{2} + x_{2} \left(x y y_{2} + x y_{2} + x\right) - y y_{2}}{x_{2} y_{2}}$$
(x2*(x + x*y2 + x*y*y2) - y*y2 - x*x2*y*y2)/(x2*y2)
Combinatorics
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x*x2 - y*y2 + x*x2*y2
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x2*y2
$$\frac{x x_{2} y_{2} + x x_{2} - y y_{2}}{x_{2} y_{2}}$$
(x*x2 - y*y2 + x*x2*y2)/(x2*y2)
Common denominator
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x*x2 - y*y2
x + -----------
x2*y2
$$x + \frac{x x_{2} - y y_{2}}{x_{2} y_{2}}$$
x + (x*x2 - y*y2)/(x2*y2)