Fraction decomposition
[src]
97/128 - 5567/(128*(-1 + 8*n)^2) + 209/(64*(-1 + 8*n))
$$\frac{97}{128} + \frac{209}{64 \left(8 n - 1\right)} - \frac{5567}{128 \left(8 n - 1\right)^{2}}$$
97 5567 209
--- - --------------- + -------------
128 2 64*(-1 + 8*n)
128*(-1 + 8*n)
General simplification
[src]
2
-92 + 28*n + 97*n
--------------------
/ 2\
2*\1 - 16*n + 64*n /
$$\frac{97 n^{2} + 28 n - 92}{2 \left(64 n^{2} - 16 n + 1\right)}$$
(-92 + 28*n + 97*n^2)/(2*(1 - 16*n + 64*n^2))
4.0*(1.0 - 4.0/(-2.0 + 16.0*n))/(-2.0 + 16.0*n) + 8.0*(1.0 - 8.0/(-2.0 + 16.0*n))/(-2.0 + 16.0*n) + (1.0 - (-2.0 + n)/(-2.0 + 16.0*n))*(-2.0 + n)/(-2.0 + 16.0*n) + (1.0 - (-2.0 + 4.0*n)/(-2.0 + 16.0*n))*(-2.0 + 4.0*n)/(-2.0 + 16.0*n) + (1.0 - (-10.0 + 5.0*n)/(-2.0 + 16.0*n))*(-10.0 + 5.0*n)/(-2.0 + 16.0*n) + 2.0*n*(1.0 - 2.0*n/(-2.0 + 16.0*n))/(-2.0 + 16.0*n) + 4.0*n*(1.0 - 4.0*n/(-2.0 + 16.0*n))/(-2.0 + 16.0*n)
4.0*(1.0 - 4.0/(-2.0 + 16.0*n))/(-2.0 + 16.0*n) + 8.0*(1.0 - 8.0/(-2.0 + 16.0*n))/(-2.0 + 16.0*n) + (1.0 - (-2.0 + n)/(-2.0 + 16.0*n))*(-2.0 + n)/(-2.0 + 16.0*n) + (1.0 - (-2.0 + 4.0*n)/(-2.0 + 16.0*n))*(-2.0 + 4.0*n)/(-2.0 + 16.0*n) + (1.0 - (-10.0 + 5.0*n)/(-2.0 + 16.0*n))*(-10.0 + 5.0*n)/(-2.0 + 16.0*n) + 2.0*n*(1.0 - 2.0*n/(-2.0 + 16.0*n))/(-2.0 + 16.0*n) + 4.0*n*(1.0 - 4.0*n/(-2.0 + 16.0*n))/(-2.0 + 16.0*n)
Rational denominator
[src]
-104 + 192*n + (-10 + 5*n)*(8 + 11*n) + 2*n*(-2 + 14*n) + 4*n*(-2 + 12*n) + 12*n*(-2 + 4*n) + 15*n*(-2 + n)
-----------------------------------------------------------------------------------------------------------
2
(-2 + 16*n)
$$\frac{15 n \left(n - 2\right) + 12 n \left(4 n - 2\right) + 4 n \left(12 n - 2\right) + 2 n \left(14 n - 2\right) + 192 n + \left(5 n - 10\right) \left(11 n + 8\right) - 104}{\left(16 n - 2\right)^{2}}$$
(-104 + 192*n + (-10 + 5*n)*(8 + 11*n) + 2*n*(-2 + 14*n) + 4*n*(-2 + 12*n) + 12*n*(-2 + 4*n) + 15*n*(-2 + n))/(-2 + 16*n)^2
97 -5985 + 3344*n
--- + ----------------------
128 2
128 - 2048*n + 8192*n
$$\frac{3344 n - 5985}{8192 n^{2} - 2048 n + 128} + \frac{97}{128}$$
97/128 + (-5985 + 3344*n)/(128 - 2048*n + 8192*n^2)
Combining rational expressions
[src]
-104 + 192*n + n*(-62 + 111*n) + 4*n*(-1 + 7*n) + 5*(-2 + n)*(8 + 11*n)
-----------------------------------------------------------------------
2
4*(-1 + 8*n)
$$\frac{4 n \left(7 n - 1\right) + n \left(111 n - 62\right) + 192 n + 5 \left(n - 2\right) \left(11 n + 8\right) - 104}{4 \left(8 n - 1\right)^{2}}$$
(-104 + 192*n + n*(-62 + 111*n) + 4*n*(-1 + 7*n) + 5*(-2 + n)*(8 + 11*n))/(4*(-1 + 8*n)^2)
Assemble expression
[src]
/ 4 \ / 8 \ / -10 + 5*n\ / -2 + n \ / -2 + 4*n\ / 2*n \ / 4*n \
4*|1 - ---------| 8*|1 - ---------| |1 - ---------|*(-10 + 5*n) |1 - ---------|*(-2 + n) |1 - ---------|*(-2 + 4*n) 2*n*|1 - ---------| 4*n*|1 - ---------|
\ -2 + 16*n/ \ -2 + 16*n/ \ -2 + 16*n/ \ -2 + 16*n/ \ -2 + 16*n/ \ -2 + 16*n/ \ -2 + 16*n/
----------------- + ----------------- + --------------------------- + ------------------------ + -------------------------- + ------------------- + -------------------
-2 + 16*n -2 + 16*n -2 + 16*n -2 + 16*n -2 + 16*n -2 + 16*n -2 + 16*n
$$\frac{4 n \left(- \frac{4 n}{16 n - 2} + 1\right)}{16 n - 2} + \frac{2 n \left(- \frac{2 n}{16 n - 2} + 1\right)}{16 n - 2} + \frac{8 \left(1 - \frac{8}{16 n - 2}\right)}{16 n - 2} + \frac{4 \left(1 - \frac{4}{16 n - 2}\right)}{16 n - 2} + \frac{\left(n - 2\right) \left(- \frac{n - 2}{16 n - 2} + 1\right)}{16 n - 2} + \frac{\left(4 n - 2\right) \left(- \frac{4 n - 2}{16 n - 2} + 1\right)}{16 n - 2} + \frac{\left(5 n - 10\right) \left(- \frac{5 n - 10}{16 n - 2} + 1\right)}{16 n - 2}$$
4*(1 - 4/(-2 + 16*n))/(-2 + 16*n) + 8*(1 - 8/(-2 + 16*n))/(-2 + 16*n) + (1 - (-10 + 5*n)/(-2 + 16*n))*(-10 + 5*n)/(-2 + 16*n) + (1 - (-2 + n)/(-2 + 16*n))*(-2 + n)/(-2 + 16*n) + (1 - (-2 + 4*n)/(-2 + 16*n))*(-2 + 4*n)/(-2 + 16*n) + 2*n*(1 - 2*n/(-2 + 16*n))/(-2 + 16*n) + 4*n*(1 - 4*n/(-2 + 16*n))/(-2 + 16*n)
2
-92 + 28*n + 97*n
------------------
2
2*(-1 + 8*n)
$$\frac{97 n^{2} + 28 n - 92}{2 \left(8 n - 1\right)^{2}}$$
(-92 + 28*n + 97*n^2)/(2*(-1 + 8*n)^2)
16 64 / 2 - n \ / 2 - 4*n \ / 10 - 5*n\ / 2*n \ / 4*n \
4 - --------- 8 - --------- |1 + ---------|*(-2 + n) |1 + ---------|*(-2 + 4*n) |1 + ---------|*(-10 + 5*n) 2*n*|1 - ---------| 4*n*|1 - ---------|
-2 + 16*n -2 + 16*n \ -2 + 16*n/ \ -2 + 16*n/ \ -2 + 16*n/ \ -2 + 16*n/ \ -2 + 16*n/
------------- + ------------- + ------------------------ + -------------------------- + --------------------------- + ------------------- + -------------------
-2 + 16*n -2 + 16*n -2 + 16*n -2 + 16*n -2 + 16*n -2 + 16*n -2 + 16*n
$$\frac{4 n \left(- \frac{4 n}{16 n - 2} + 1\right)}{16 n - 2} + \frac{2 n \left(- \frac{2 n}{16 n - 2} + 1\right)}{16 n - 2} + \frac{4 - \frac{16}{16 n - 2}}{16 n - 2} + \frac{8 - \frac{64}{16 n - 2}}{16 n - 2} + \frac{\left(n - 2\right) \left(\frac{2 - n}{16 n - 2} + 1\right)}{16 n - 2} + \frac{\left(4 n - 2\right) \left(\frac{2 - 4 n}{16 n - 2} + 1\right)}{16 n - 2} + \frac{\left(5 n - 10\right) \left(\frac{10 - 5 n}{16 n - 2} + 1\right)}{16 n - 2}$$
/ 4 \ / 8 \ / -10 + 5*n\ / -2 + n \ / -2 + 4*n\ / 2*n \ / 4*n \
4*|1 - ---------| 8*|1 - ---------| |1 - ---------|*(-10 + 5*n) |1 - ---------|*(-2 + n) |1 - ---------|*(-2 + 4*n) 2*n*|1 - ---------| 4*n*|1 - ---------|
\ -2 + 16*n/ \ -2 + 16*n/ \ -2 + 16*n/ \ -2 + 16*n/ \ -2 + 16*n/ \ -2 + 16*n/ \ -2 + 16*n/
----------------- + ----------------- + --------------------------- + ------------------------ + -------------------------- + ------------------- + -------------------
-2 + 16*n -2 + 16*n -2 + 16*n -2 + 16*n -2 + 16*n -2 + 16*n -2 + 16*n
$$\frac{4 n \left(- \frac{4 n}{16 n - 2} + 1\right)}{16 n - 2} + \frac{2 n \left(- \frac{2 n}{16 n - 2} + 1\right)}{16 n - 2} + \frac{8 \left(1 - \frac{8}{16 n - 2}\right)}{16 n - 2} + \frac{4 \left(1 - \frac{4}{16 n - 2}\right)}{16 n - 2} + \frac{\left(n - 2\right) \left(- \frac{n - 2}{16 n - 2} + 1\right)}{16 n - 2} + \frac{\left(4 n - 2\right) \left(- \frac{4 n - 2}{16 n - 2} + 1\right)}{16 n - 2} + \frac{\left(5 n - 10\right) \left(- \frac{5 n - 10}{16 n - 2} + 1\right)}{16 n - 2}$$
4*(1 - 4/(-2 + 16*n))/(-2 + 16*n) + 8*(1 - 8/(-2 + 16*n))/(-2 + 16*n) + (1 - (-10 + 5*n)/(-2 + 16*n))*(-10 + 5*n)/(-2 + 16*n) + (1 - (-2 + n)/(-2 + 16*n))*(-2 + n)/(-2 + 16*n) + (1 - (-2 + 4*n)/(-2 + 16*n))*(-2 + 4*n)/(-2 + 16*n) + 2*n*(1 - 2*n/(-2 + 16*n))/(-2 + 16*n) + 4*n*(1 - 4*n/(-2 + 16*n))/(-2 + 16*n)
/ 4 \ / 8 \ / -10 + 5*n\ / -2 + n \ / -2 + 4*n\ / 2*n \ / 4*n \
4*|1 - ---------| 8*|1 - ---------| |1 - ---------|*(-10 + 5*n) |1 - ---------|*(-2 + n) |1 - ---------|*(-2 + 4*n) 2*n*|1 - ---------| 4*n*|1 - ---------|
\ -2 + 16*n/ \ -2 + 16*n/ \ -2 + 16*n/ \ -2 + 16*n/ \ -2 + 16*n/ \ -2 + 16*n/ \ -2 + 16*n/
----------------- + ----------------- + --------------------------- + ------------------------ + -------------------------- + ------------------- + -------------------
-2 + 16*n -2 + 16*n -2 + 16*n -2 + 16*n -2 + 16*n -2 + 16*n -2 + 16*n
$$\frac{4 n \left(- \frac{4 n}{16 n - 2} + 1\right)}{16 n - 2} + \frac{2 n \left(- \frac{2 n}{16 n - 2} + 1\right)}{16 n - 2} + \frac{8 \left(1 - \frac{8}{16 n - 2}\right)}{16 n - 2} + \frac{4 \left(1 - \frac{4}{16 n - 2}\right)}{16 n - 2} + \frac{\left(n - 2\right) \left(- \frac{n - 2}{16 n - 2} + 1\right)}{16 n - 2} + \frac{\left(4 n - 2\right) \left(- \frac{4 n - 2}{16 n - 2} + 1\right)}{16 n - 2} + \frac{\left(5 n - 10\right) \left(- \frac{5 n - 10}{16 n - 2} + 1\right)}{16 n - 2}$$
4*(1 - 4/(-2 + 16*n))/(-2 + 16*n) + 8*(1 - 8/(-2 + 16*n))/(-2 + 16*n) + (1 - (-10 + 5*n)/(-2 + 16*n))*(-10 + 5*n)/(-2 + 16*n) + (1 - (-2 + n)/(-2 + 16*n))*(-2 + n)/(-2 + 16*n) + (1 - (-2 + 4*n)/(-2 + 16*n))*(-2 + 4*n)/(-2 + 16*n) + 2*n*(1 - 2*n/(-2 + 16*n))/(-2 + 16*n) + 4*n*(1 - 4*n/(-2 + 16*n))/(-2 + 16*n)