Mister Exam
Least common denominator y-b/(a-a*b)-(y-a)/a*b-b
The solution
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b y - a
y - ------- - -----*b - b
a - a*b a
$$- b + \left(- b \frac{- a + y}{a} + \left(- \frac{b}{- a b + a} + y\right)\right)$$
y - b/(a - a*b) - (y - a)/a*b - b
General simplification
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b + a*(-1 + b)*(y - b) + b*(-1 + b)*(a - y)
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a*(-1 + b)
$$\frac{a \left(- b + y\right) \left(b - 1\right) + b \left(a - y\right) \left(b - 1\right) + b}{a \left(b - 1\right)}$$
(b + a*(-1 + b)*(y - b) + b*(-1 + b)*(a - y))/(a*(-1 + b))
Powers
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b b*(y - a)
y - b - ------- - ---------
a - a*b a
$$- b - \frac{b}{- a b + a} + y - \frac{b \left(- a + y\right)}{a}$$
y - b - b/(a - a*b) - b*(y - a)/a
Trigonometric part
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b b*(y - a)
y - b - ------- - ---------
a - a*b a
$$- b - \frac{b}{- a b + a} + y - \frac{b \left(- a + y\right)}{a}$$
y - b - b/(a - a*b) - b*(y - a)/a
Common denominator
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2
-b + y*b - b*y
y - ---------------
-a + a*b
$$y - \frac{b^{2} y - b y - b}{a b - a}$$
y - (-b + y*b^2 - b*y)/(-a + a*b)
Combining rational expressions
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-b + a*y*(1 - b) - a*b*(1 - b) - b*(1 - b)*(y - a)
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a*(1 - b)
$$\frac{- a b \left(1 - b\right) + a y \left(1 - b\right) - b \left(1 - b\right) \left(- a + y\right) - b}{a \left(1 - b\right)}$$
(-b + a*y*(1 - b) - a*b*(1 - b) - b*(1 - b)*(y - a))/(a*(1 - b))
Combinatorics
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2
b + b*y - a*y - y*b + a*b*y
----------------------------
a*(-1 + b)
$$\frac{a b y - a y - b^{2} y + b y + b}{a \left(b - 1\right)}$$
(b + b*y - a*y - y*b^2 + a*b*y)/(a*(-1 + b))
Assemble expression
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b b*(y - a)
y - b - --------- - ---------
a*(1 - b) a
$$- b + y - \frac{b \left(- a + y\right)}{a} - \frac{b}{a \left(1 - b\right)}$$
b b*(y - a)
y - b - ------- - ---------
a - a*b a
$$- b - \frac{b}{- a b + a} + y - \frac{b \left(- a + y\right)}{a}$$
/ 1 y - a\
y + b*|-1 - ------- - -----|
\ a - a*b a /
$$b \left(-1 - \frac{1}{- a b + a} - \frac{- a + y}{a}\right) + y$$
b
- ----- - b*(y - a)
1 - b
y - b + -------------------
a
$$- b + y + \frac{- b \left(- a + y\right) - \frac{b}{1 - b}}{a}$$
y - b + (-b/(1 - b) - b*(y - a))/a
Rational denominator
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a*(-b + y*(a - a*b)) - a*b*(a - a*b) - b*(a - a*b)*(y - a)
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a*(a - a*b)
$$\frac{- a b \left(- a b + a\right) + a \left(- b + y \left(- a b + a\right)\right) - b \left(- a + y\right) \left(- a b + a\right)}{a \left(- a b + a\right)}$$
(a*(-b + y*(a - a*b)) - a*b*(a - a*b) - b*(a - a*b)*(y - a))/(a*(a - a*b))