Mister Exam

# Least common denominator factorial(n)/factorial(n+1)-(n-1)/factorial(n)

An expression to simplify:

### The solution

You have entered [src]
n!      n - 1
-------- - -----
(n + 1)!     n!
$$- \frac{n - 1}{n!} + \frac{n!}{\left(n + 1\right)!}$$
factorial(n)/factorial(n + 1) - (n - 1)/factorial(n)
factorial(n)/factorial(n + 1) - (-1.0 + n)/factorial(n)
factorial(n)/factorial(n + 1) - (-1.0 + n)/factorial(n)
Rational denominator [src]
2
n!  - n*(1 + n)! + (1 + n)!
---------------------------
n!*(1 + n)!
$$\frac{- n \left(n + 1\right)! + n!^{2} + \left(n + 1\right)!}{n! \left(n + 1\right)!}$$
(factorial(n)^2 - n*factorial(1 + n) + factorial(1 + n))/(factorial(n)*factorial(1 + n))
Common denominator [src]
/    2                        \
-\- n!  - (1 + n)! + n*(1 + n)!/
---------------------------------
n!*(1 + n)!
$$- \frac{n \left(n + 1\right)! - n!^{2} - \left(n + 1\right)!}{n! \left(n + 1\right)!}$$
-(-factorial(n)^2 - factorial(1 + n) + n*factorial(1 + n))/(factorial(n)*factorial(1 + n))
Powers [src]
1 - n      n!
----- + --------
n!    (1 + n)!
$$\frac{1 - n}{n!} + \frac{n!}{\left(n + 1\right)!}$$
(1 - n)/factorial(n) + factorial(n)/factorial(1 + n)
Combinatorics [src]
-(-Gamma(n) + n*Gamma(1 + n) - Gamma(n)*Gamma(1 + n))
------------------------------------------------------
Gamma(n)*Gamma(2 + n)
$$- \frac{n \Gamma\left(n + 1\right) - \Gamma\left(n\right) \Gamma\left(n + 1\right) - \Gamma\left(n\right)}{\Gamma\left(n\right) \Gamma\left(n + 2\right)}$$
-(-gamma(n) + n*gamma(1 + n) - gamma(n)*gamma(1 + n))/(gamma(n)*gamma(2 + n))
Combining rational expressions [src]
2
n!  - (-1 + n)*(1 + n)!
-----------------------
n!*(1 + n)!
$$\frac{- \left(n - 1\right) \left(n + 1\right)! + n!^{2}}{n! \left(n + 1\right)!}$$
(factorial(n)^2 - (-1 + n)*factorial(1 + n))/(factorial(n)*factorial(1 + n))
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