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