Mister Exam
Least common denominator n+6/(4*n+8)-n+2/(4*n-8)+5/(n^2-4)
The solution
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6 2 5
n + ------- - n + ------- + ------
4*n + 8 4*n - 8 2
n - 4
$$\left(\left(- n + \left(n + \frac{6}{4 n + 8}\right)\right) + \frac{2}{4 n - 8}\right) + \frac{5}{n^{2} - 4}$$
n + 6/(4*n + 8) - n + 2/(4*n - 8) + 5/(n^2 - 4)
Fraction decomposition
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1/(4*(2 + n)) + 7/(4*(-2 + n))
$$\frac{1}{4 \left(n + 2\right)} + \frac{7}{4 \left(n - 2\right)}$$
1 7 --------- + ---------- 4*(2 + n) 4*(-2 + n)
General simplification
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3 + 2*n
-------
2
-4 + n
$$\frac{2 n + 3}{n^{2} - 4}$$
(3 + 2*n)/(-4 + n^2)
Rational denominator
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/ 2\
(-32 + 32*n)*\-4 + n / + 5*(-8 + 4*n)*(8 + 4*n)
-----------------------------------------------
/ 2\
(-8 + 4*n)*\-4 + n /*(8 + 4*n)
$$\frac{5 \left(4 n - 8\right) \left(4 n + 8\right) + \left(32 n - 32\right) \left(n^{2} - 4\right)}{\left(4 n - 8\right) \left(4 n + 8\right) \left(n^{2} - 4\right)}$$
((-32 + 32*n)*(-4 + n^2) + 5*(-8 + 4*n)*(8 + 4*n))/((-8 + 4*n)*(-4 + n^2)*(8 + 4*n))
Numerical answer
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2.0/(-8.0 + 4.0*n) + 6.0/(8.0 + 4.0*n) + 5.0/(-4.0 + n^2)
2.0/(-8.0 + 4.0*n) + 6.0/(8.0 + 4.0*n) + 5.0/(-4.0 + n^2)
Combinatorics
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3 + 2*n ---------------- (-2 + n)*(2 + n)
$$\frac{2 n + 3}{\left(n - 2\right) \left(n + 2\right)}$$
(3 + 2*n)/((-2 + n)*(2 + n))
Common denominator
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3 + 2*n
-------
2
-4 + n
$$\frac{2 n + 3}{n^{2} - 4}$$
(3 + 2*n)/(-4 + n^2)
Trigonometric part
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2 5 6
-------- + ------- + -------
-8 + 4*n 2 8 + 4*n
-4 + n
$$\frac{5}{n^{2} - 4} + \frac{6}{4 n + 8} + \frac{2}{4 n - 8}$$
2/(-8 + 4*n) + 5/(-4 + n^2) + 6/(8 + 4*n)
Powers
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2 5 6
-------- + ------- + -------
-8 + 4*n 2 8 + 4*n
-4 + n
$$\frac{5}{n^{2} - 4} + \frac{6}{4 n + 8} + \frac{2}{4 n - 8}$$
2/(-8 + 4*n) + 5/(-4 + n^2) + 6/(8 + 4*n)
Assemble expression
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2 5 6
-------- + ------- + -------
-8 + 4*n 2 8 + 4*n
-4 + n
$$\frac{5}{n^{2} - 4} + \frac{6}{4 n + 8} + \frac{2}{4 n - 8}$$
2/(-8 + 4*n) + 5/(-4 + n^2) + 6/(8 + 4*n)
Combining rational expressions
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/ 2\
2*(-1 + n)*\-4 + n / + 5*(-2 + n)*(2 + n)
-----------------------------------------
/ 2\
\-4 + n /*(-2 + n)*(2 + n)
$$\frac{5 \left(n - 2\right) \left(n + 2\right) + 2 \left(n - 1\right) \left(n^{2} - 4\right)}{\left(n - 2\right) \left(n + 2\right) \left(n^{2} - 4\right)}$$
(2*(-1 + n)*(-4 + n^2) + 5*(-2 + n)*(2 + n))/((-4 + n^2)*(-2 + n)*(2 + n))