Mister Exam
Least common denominator a3*b3/a3-a2*b*b2-a2/4*ab2
The solution
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a3*b3 a2 2 ----- - a2*b*b2 - --*a*b a3 4
$$- b^{2} a \frac{a_{2}}{4} + \left(- b_{2} a_{2} b + \frac{a_{3} b_{3}}{a_{3}}\right)$$
(a3*b3)/a3 - a2*b*b2 - (a2/4)*a*b^2
General simplification
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2
a*a2*b
b3 - a2*b*b2 - -------
4
$$- \frac{a a_{2} b^{2}}{4} - a_{2} b b_{2} + b_{3}$$
b3 - a2*b*b2 - a*a2*b^2/4
Common denominator
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2
a*a2*b
b3 - a2*b*b2 - -------
4
$$- \frac{a a_{2} b^{2}}{4} - a_{2} b b_{2} + b_{3}$$
b3 - a2*b*b2 - a*a2*b^2/4
Powers
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2
a*a2*b
b3 - a2*b*b2 - -------
4
$$- \frac{a a_{2} b^{2}}{4} - a_{2} b b_{2} + b_{3}$$
b3 - a2*b*b2 - a*a2*b^2/4
Rational denominator
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2
4*a3*b3 - a*a2*a3*b - 4*a2*a3*b*b2
-----------------------------------
4*a3
$$\frac{- a a_{2} a_{3} b^{2} - 4 a_{2} a_{3} b b_{2} + 4 a_{3} b_{3}}{4 a_{3}}$$
(4*a3*b3 - a*a2*a3*b^2 - 4*a2*a3*b*b2)/(4*a3)
Combinatorics
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2
a*a2*b
b3 - a2*b*b2 - -------
4
$$- \frac{a a_{2} b^{2}}{4} - a_{2} b b_{2} + b_{3}$$
b3 - a2*b*b2 - a*a2*b^2/4
Combining rational expressions
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2
4*b3 - a*a2*b - 4*a2*b*b2
--------------------------
4
$$\frac{- a a_{2} b^{2} - 4 a_{2} b b_{2} + 4 b_{3}}{4}$$
(4*b3 - a*a2*b^2 - 4*a2*b*b2)/4
Assemble expression
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/ 2\
| a*b |
b3 + a2*|-b*b2 - ----|
\ 4 /
$$a_{2} \left(- \frac{a b^{2}}{4} - b b_{2}\right) + b_{3}$$
2
a*a2*b
b3 - a2*b*b2 - -------
4
$$- \frac{a a_{2} b^{2}}{4} - a_{2} b b_{2} + b_{3}$$
b3 - a2*b*b2 - a*a2*b^2/4
Trigonometric part
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2
a*a2*b
b3 - a2*b*b2 - -------
4
$$- \frac{a a_{2} b^{2}}{4} - a_{2} b b_{2} + b_{3}$$
b3 - a2*b*b2 - a*a2*b^2/4