Mister Exam
Expression simplification/
Fraction Decomposition into the simple/
(u^2-4*u+16)/(16*u^2-1)*(4*u^2+u)/(u^3+64)
How do you (u^2-4*u+16)/(16*u^2-1)*(4*u^2+u)/(u^3+64) in partial fractions?
The solution
You have entered
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2
u - 4*u + 16 / 2 \
-------------*\4*u + u/
2
16*u - 1
------------------------
3
u + 64
$$\frac{\frac{\left(u^{2} - 4 u\right) + 16}{16 u^{2} - 1} \left(4 u^{2} + u\right)}{u^{3} + 64}$$
(((u^2 - 4*u + 16)/(16*u^2 - 1))*(4*u^2 + u))/(u^3 + 64)
Fraction decomposition
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1/(17*(-1 + 4*u)) + 4/(17*(4 + u))
$$\frac{1}{17 \left(4 u - 1\right)} + \frac{4}{17 \left(u + 4\right)}$$
1 4 ------------- + ---------- 17*(-1 + 4*u) 17*(4 + u)
General simplification
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u
----------------
2
-4 + 4*u + 15*u
$$\frac{u}{4 u^{2} + 15 u - 4}$$
u/(-4 + 4*u^2 + 15*u)
Combining rational expressions
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u*(1 + 4*u)*(16 + u*(-4 + u))
-----------------------------
/ 2\ / 3\
\-1 + 16*u /*\64 + u /
$$\frac{u \left(4 u + 1\right) \left(u \left(u - 4\right) + 16\right)}{\left(16 u^{2} - 1\right) \left(u^{3} + 64\right)}$$
u*(1 + 4*u)*(16 + u*(-4 + u))/((-1 + 16*u^2)*(64 + u^3))
Numerical answer
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(u + 4.0*u^2)*(16.0 + u^2 - 4.0*u)/((64.0 + u^3)*(-1.0 + 16.0*u^2))
(u + 4.0*u^2)*(16.0 + u^2 - 4.0*u)/((64.0 + u^3)*(-1.0 + 16.0*u^2))
Powers
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/ 2\ / 2 \ \u + 4*u /*\16 + u - 4*u/ -------------------------- / 2\ / 3\ \-1 + 16*u /*\64 + u /
$$\frac{\left(4 u^{2} + u\right) \left(u^{2} - 4 u + 16\right)}{\left(16 u^{2} - 1\right) \left(u^{3} + 64\right)}$$
(u + 4*u^2)*(16 + u^2 - 4*u)/((-1 + 16*u^2)*(64 + u^3))
Combinatorics
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u ------------------ (-1 + 4*u)*(4 + u)
$$\frac{u}{\left(u + 4\right) \left(4 u - 1\right)}$$
u/((-1 + 4*u)*(4 + u))
Rational denominator
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/ 2\ / 2 \ \u + 4*u /*\16 + u - 4*u/ -------------------------- / 2\ / 3\ \-1 + 16*u /*\64 + u /
$$\frac{\left(4 u^{2} + u\right) \left(u^{2} - 4 u + 16\right)}{\left(16 u^{2} - 1\right) \left(u^{3} + 64\right)}$$
(u + 4*u^2)*(16 + u^2 - 4*u)/((-1 + 16*u^2)*(64 + u^3))
Assemble expression
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/ 2\ / 2 \ \u + 4*u /*\16 + u - 4*u/ -------------------------- / 2\ / 3\ \-1 + 16*u /*\64 + u /
$$\frac{\left(4 u^{2} + u\right) \left(u^{2} - 4 u + 16\right)}{\left(16 u^{2} - 1\right) \left(u^{3} + 64\right)}$$
(u + 4*u^2)*(16 + u^2 - 4*u)/((-1 + 16*u^2)*(64 + u^3))
Common denominator
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u
----------------
2
-4 + 4*u + 15*u
$$\frac{u}{4 u^{2} + 15 u - 4}$$
u/(-4 + 4*u^2 + 15*u)
Trigonometric part
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/ 2\ / 2 \ \u + 4*u /*\16 + u - 4*u/ -------------------------- / 2\ / 3\ \-1 + 16*u /*\64 + u /
$$\frac{\left(4 u^{2} + u\right) \left(u^{2} - 4 u + 16\right)}{\left(16 u^{2} - 1\right) \left(u^{3} + 64\right)}$$
(u + 4*u^2)*(16 + u^2 - 4*u)/((-1 + 16*u^2)*(64 + u^3))