Mister Exam
How do you (pi*a^2+pi/4)/(pi*a^2+pi/2) in partial fractions?
The solution
You have entered
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2 pi
pi*a + --
4
----------
2 pi
pi*a + --
2
$$\frac{\pi a^{2} + \frac{\pi}{4}}{\pi a^{2} + \frac{\pi}{2}}$$
(pi*a^2 + pi/4)/(pi*a^2 + pi/2)
General simplification
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2 1 + 4*a ------------ / 2\ 2*\1 + 2*a /
$$\frac{4 a^{2} + 1}{2 \left(2 a^{2} + 1\right)}$$
(1 + 4*a^2)/(2*(1 + 2*a^2))
Fraction decomposition
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1 - 1/(2*(1 + 2*a^2))
$$1 - \frac{1}{2 \left(2 a^{2} + 1\right)}$$
1
1 - ------------
/ 2\
2*\1 + 2*a /
Rational denominator
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2
2*pi + 8*pi*a
--------------
2
4*pi + 8*pi*a
$$\frac{8 \pi a^{2} + 2 \pi}{8 \pi a^{2} + 4 \pi}$$
(2*pi + 8*pi*a^2)/(4*pi + 8*pi*a^2)
Combinatorics
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2 1 + 4*a ------------ / 2\ 2*\1 + 2*a /
$$\frac{4 a^{2} + 1}{2 \left(2 a^{2} + 1\right)}$$
(1 + 4*a^2)/(2*(1 + 2*a^2))
Combining rational expressions
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2 1 + 4*a ------------ / 2\ 2*\1 + 2*a /
$$\frac{4 a^{2} + 1}{2 \left(2 a^{2} + 1\right)}$$
(1 + 4*a^2)/(2*(1 + 2*a^2))
Numerical answer
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(0.785398163397448 + 3.14159265358979*a^2)/(1.5707963267949 + 3.14159265358979*a^2)
(0.785398163397448 + 3.14159265358979*a^2)/(1.5707963267949 + 3.14159265358979*a^2)