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