Mister Exam
Factor polynomial y*y/x-x^2+x*y/x-y^2
The solution
You have entered
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y*y 2 x*y 2 --- - x + --- - y x x
$$- y^{2} + \left(\left(- x^{2} + \frac{y y}{x}\right) + \frac{x y}{x}\right)$$
(y*y)/x - x^2 + (x*y)/x - y^2
General simplification
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2
2 2 y
y - x - y + --
x
$$- x^{2} - y^{2} + y + \frac{y^{2}}{x}$$
y - x^2 - y^2 + y^2/x
Combining rational expressions
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2 3 2
y - x + x*y - x*y
--------------------
x
$$\frac{- x^{3} - x y^{2} + x y + y^{2}}{x}$$
(y^2 - x^3 + x*y - x*y^2)/x
Combinatorics
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/ 3 2 2 \
-\x - y + x*y - x*y/
------------------------
x
$$- \frac{x^{3} + x y^{2} - x y - y^{2}}{x}$$
-(x^3 - y^2 + x*y^2 - x*y)/x
Common denominator
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2
2 2 y
y - x - y + --
x
$$- x^{2} - y^{2} + y + \frac{y^{2}}{x}$$
y - x^2 - y^2 + y^2/x
Rational denominator
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2 3 2
y - x + x*y - x*y
--------------------
x
$$\frac{- x^{3} - x y^{2} + x y + y^{2}}{x}$$
(y^2 - x^3 + x*y - x*y^2)/x
Trigonometric part
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2
2 2 y
y - x - y + --
x
$$- x^{2} - y^{2} + y + \frac{y^{2}}{x}$$
y - x^2 - y^2 + y^2/x
Powers
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2
2 2 y
y - x - y + --
x
$$- x^{2} - y^{2} + y + \frac{y^{2}}{x}$$
y - x^2 - y^2 + y^2/x
Assemble expression
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2 2 / 1\
y - x + y *|-1 + -|
\ x/
$$- x^{2} + y^{2} \left(-1 + \frac{1}{x}\right) + y$$
2
2 2 y
y - x - y + --
x
$$- x^{2} - y^{2} + y + \frac{y^{2}}{x}$$
y - x^2 - y^2 + y^2/x