### Related

##### factcomb-minfactorial-ratsimp

solve_rec(a[n]=a[n-1]...

2*x*(x+1)*y[x] - (x^...

solve_rec(%, y[x], y...

Calculate

##### factcomb-false-rat-sumsplitfact

p: (n-1)!/((k-1)!*(n-...

q: factcomb(p*(k-2)!*...

rat(q);

Calculate

##### factcomb-false-sumsplitfact

f(n,k):=n!^2/(k!*(n-k...

p: factcomb(f(n,k)-(n...

Calculate

##### factcomb-false-sumsplitfact

f(n,k):=n!^2/(k!*(n-k...

p: factcomb(f(n,k)-(n...

Calculate

##### factcomb-false-rat-sumsplitfact

p: (n-1)!/((k-1)!*(n-...

q: factcomb(p*(k-2)!*...

rat(q);

Calculate

##### factcomb-false-sumsplitfact

f(n,k):=n!^3/(k!*(n-k...

p: factcomb(f(n,k)-(n...

Calculate

##### factcomb-false-rat-sumsplitfact

f(n,k):=n!^3/(k!^3*(n...

sumsplitfact:false;

p: factcomb(rat(f(n,k...

Calculate

##### factcomb-pochhammer

factcomb(pochhammer(a...

Calculate

##### factcomb-false-num-rat-sumsplitfact

p: (n-1)!/((k-1)!*(n-...

q: factcomb(p*(k-2)!*...

num(q);

Calculate

##### factcomb-false-sumsplitfact

p: (n-1)!/((k-1)!*(n-...

q: factcomb(p*(k-2)!*...

Calculate

### factcomb

Run Example
```(%i1)factcomb(3/(x+y)^2 - 4/(x-y)^2 + 5/(x^2-y^2));
5         3          4
(%o1)                    ------- + -------- - --------
2    2          2          2
x  - y    (y + x)    (x - y)
(%i2) ```
Run Example
```p: (n-1)!/((k-1)!*(n-k)!)-k*(n-2)!/((k-1)!*(n-k-1)!)-(n-2)!/((k-2)!*(n-k)!);
(n - 1)!            (n - 2)!             k (n - 2)!
(%o1)    ----------------- - ----------------- - ---------------------
(k - 1)! (n - k)!   (k - 2)! (n - k)!   (k - 1)! (n - k - 1)!
(%i2) q: factcomb(p*(k-2)!*(n-k-1)!/(n-2)!), sumsplitfact:false;
n - 1          1       k
(%o2)                   --------------- - ----- - -----
(k - 1) (n - k)   n - k   k - 1
(%i3) num(q);
n - 1          1       k
(%o3)                   --------------- - ----- - -----
(k - 1) (n - k)   n - k   k - 1
(%i4) rat(q);
(%o4)/R/                              - 1
(%i5) ```
Run Example
```f(n,k):=n!^3/k!^3*(n-k)!^3;
3
n!          3
(%o1)                      f(n, k) := --- (n - k)!
3
k!
(%i2) sumsplitfact:false;
(%o2)                                false
(%i3) p: factcomb(f(n,k)-(n^2+n*k+k^2)/(n-k)^2*f(n-1,k)-f(n-1,k-1));
5        3         3             3
n  (n - k)  (n - 1)!  (n - k - 1)!
(%o3) -------------------------------------------------
3         3  2      4         3      5         3
k  (k - 1)!  n  - 2 k  (k - 1)!  n + k  (k - 1)!
4        3         3             3
2 k n  (n - k)  (n - 1)!  (n - k - 1)!
- -------------------------------------------------
3         3  2      4         3      5         3
k  (k - 1)!  n  - 2 k  (k - 1)!  n + k  (k - 1)!
2  3        3         3             3
k  n  (n - k)  (n - 1)!  (n - k - 1)!
+ -------------------------------------------------
3         3  2      4         3      5         3
k  (k - 1)!  n  - 2 k  (k - 1)!  n + k  (k - 1)!
2         3             3
n  (n - 1)!  (n - k - 1)!
- -------------------------------------------------
3         3  2      4         3      5         3
k  (k - 1)!  n  - 2 k  (k - 1)!  n + k  (k - 1)!
3             3
k n (n - 1)!  (n - k - 1)!
- -------------------------------------------------
3         3  2      4         3      5         3
k  (k - 1)!  n  - 2 k  (k - 1)!  n + k  (k - 1)!
2         3             3
k  (n - 1)!  (n - k - 1)!
- -------------------------------------------------
3         3  2      4         3      5         3
k  (k - 1)!  n  - 2 k  (k - 1)!  n + k  (k - 1)!
3         3             3
(n - k)  (n - 1)!  (n - k - 1)!
- --------------------------------
3
(k - 1)!
(%i4) ```

### Related Help

Help for Factcomb