Mister Exam
How do you (a+4)*a/2+(4*a+16)/(4*a^2+a^3) in partial fractions?
The solution
You have entered
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(a + 4)*a 4*a + 16
--------- + ---------
2 2 3
4*a + a
$$\frac{a \left(a + 4\right)}{2} + \frac{4 a + 16}{a^{3} + 4 a^{2}}$$
((a + 4)*a)/2 + (4*a + 16)/(4*a^2 + a^3)
Fraction decomposition
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a^2/2 + 2*a + 4/a^2
$$\frac{a^{2}}{2} + 2 a + \frac{4}{a^{2}}$$
2
a 4
-- + 2*a + --
2 2
a
General simplification
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2
a 4
-- + 2*a + --
2 2
a
$$\frac{a^{2}}{2} + 2 a + \frac{4}{a^{2}}$$
a^2/2 + 2*a + 4/a^2
Rational denominator
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/ 3 2\
32 + 8*a + a*(4 + a)*\a + 4*a /
--------------------------------
3 2
2*a + 8*a
$$\frac{a \left(a + 4\right) \left(a^{3} + 4 a^{2}\right) + 8 a + 32}{2 a^{3} + 8 a^{2}}$$
(32 + 8*a + a*(4 + a)*(a^3 + 4*a^2))/(2*a^3 + 8*a^2)
Common denominator
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2
a 4
-- + 2*a + --
2 2
a
$$\frac{a^{2}}{2} + 2 a + \frac{4}{a^{2}}$$
a^2/2 + 2*a + 4/a^2
Combinatorics
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4 3
8 + a + 4*a
-------------
2
2*a
$$\frac{a^{4} + 4 a^{3} + 8}{2 a^{2}}$$
(8 + a^4 + 4*a^3)/(2*a^2)
Combining rational expressions
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3
8 + a *(4 + a)
--------------
2
2*a
$$\frac{a^{3} \left(a + 4\right) + 8}{2 a^{2}}$$
(8 + a^3*(4 + a))/(2*a^2)
Numerical answer
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(16.0 + 4.0*a)/(a^3 + 4.0*a^2) + 0.5*a*(4.0 + a)
(16.0 + 4.0*a)/(a^3 + 4.0*a^2) + 0.5*a*(4.0 + a)