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/(-4 + a) + 2*a + 2/a + 4/a^2
$$\frac{a^{2}}{2} + 2 a - \frac{2}{a - 4} + \frac{2}{a} + \frac{4}{a^{2}}$$
2
a 2 2 4
-- - ------ + 2*a + - + --
2 -4 + a a 2
a
General simplification
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5 3
-32 + a - 16*a - 8*a
----------------------
2
2*a *(-4 + a)
$$\frac{a^{5} - 16 a^{3} - 8 a - 32}{2 a^{2} \left(a - 4\right)}$$
(-32 + a^5 - 16*a^3 - 8*a)/(2*a^2*(-4 + a))
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)
Combinatorics
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/ 4 3\
(4 + a)*\-8 + a - 4*a /
------------------------
2
2*a *(-4 + a)
$$\frac{\left(a + 4\right) \left(a^{4} - 4 a^{3} - 8\right)}{2 a^{2} \left(a - 4\right)}$$
(4 + a)*(-8 + a^4 - 4*a^3)/(2*a^2*(-4 + a))
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)
Combining rational expressions
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/ a\ / 3 \
|2 + -|*\8 + a *(4 - a)/
\ 2/
------------------------
2
a *(4 - a)
$$\frac{\left(\frac{a}{2} + 2\right) \left(a^{3} \left(4 - a\right) + 8\right)}{a^{2} \left(4 - a\right)}$$
(2 + a/2)*(8 + a^3*(4 - a))/(a^2*(4 - a))
Common denominator
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2
a 16 + 4*a
-- + 2*a - ---------
2 3 2
a - 4*a
$$\frac{a^{2}}{2} + 2 a - \frac{4 a + 16}{a^{3} - 4 a^{2}}$$
a^2/2 + 2*a - (16 + 4*a)/(a^3 - 4*a^2)