Mister Exam
Least common denominator n+3/(2*n+2)-n+1/(2*n-2)+3/(n^2-1)
The solution
You have entered
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3 1 3
n + ------- - n + ------- + ------
2*n + 2 2*n - 2 2
n - 1
$$\left(\left(- n + \left(n + \frac{3}{2 n + 2}\right)\right) + \frac{1}{2 n - 2}\right) + \frac{3}{n^{2} - 1}$$
n + 3/(2*n + 2) - n + 1/(2*n - 2) + 3/(n^2 - 1)
Numerical answer
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1/(-2.0 + 2.0*n) + 3.0/(2.0 + 2.0*n) + 3.0/(-1.0 + n^2)
1/(-2.0 + 2.0*n) + 3.0/(2.0 + 2.0*n) + 3.0/(-1.0 + n^2)
Assemble expression
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1 3 3
-------- + ------- + -------
-2 + 2*n 2 2 + 2*n
-1 + n
$$\frac{3}{n^{2} - 1} + \frac{3}{2 n + 2} + \frac{1}{2 n - 2}$$
1/(-2 + 2*n) + 3/(-1 + n^2) + 3/(2 + 2*n)
Powers
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1 3 3
-------- + ------- + -------
-2 + 2*n 2 2 + 2*n
-1 + n
$$\frac{3}{n^{2} - 1} + \frac{3}{2 n + 2} + \frac{1}{2 n - 2}$$
1/(-2 + 2*n) + 3/(-1 + n^2) + 3/(2 + 2*n)
Rational denominator
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/ 2\
\-1 + n /*(-4 + 8*n) + 3*(-2 + 2*n)*(2 + 2*n)
---------------------------------------------
/ 2\
\-1 + n /*(-2 + 2*n)*(2 + 2*n)
$$\frac{3 \left(2 n - 2\right) \left(2 n + 2\right) + \left(8 n - 4\right) \left(n^{2} - 1\right)}{\left(2 n - 2\right) \left(2 n + 2\right) \left(n^{2} - 1\right)}$$
((-1 + n^2)*(-4 + 8*n) + 3*(-2 + 2*n)*(2 + 2*n))/((-1 + n^2)*(-2 + 2*n)*(2 + 2*n))
Trigonometric part
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1 3 3
-------- + ------- + -------
-2 + 2*n 2 2 + 2*n
-1 + n
$$\frac{3}{n^{2} - 1} + \frac{3}{2 n + 2} + \frac{1}{2 n - 2}$$
1/(-2 + 2*n) + 3/(-1 + n^2) + 3/(2 + 2*n)
Combining rational expressions
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/ 2\
\-1 + n /*(-1 + 2*n) + 3*(1 + n)*(-1 + n)
-----------------------------------------
/ 2\
(1 + n)*(-1 + n)*\-1 + n /
$$\frac{3 \left(n - 1\right) \left(n + 1\right) + \left(2 n - 1\right) \left(n^{2} - 1\right)}{\left(n - 1\right) \left(n + 1\right) \left(n^{2} - 1\right)}$$
((-1 + n^2)*(-1 + 2*n) + 3*(1 + n)*(-1 + n))/((1 + n)*(-1 + n)*(-1 + n^2))