Mister Exam
Other calculators
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How to use it?
- Factor polynomial:
- y^5+y^3+y^2+1
- a^2+8*a+16
- x^4-81
- y^2-81
- Least common denominator:
- k1/(1+k1*(-k2*k3*k3/((t3^2*s^2+2*t3*s*e+1)*(t2*s+1))+1/(t1*s+1)))
- factorial(n)/factorial(n+1)-(n-1)/factorial(n)
- (x1/3-y1/3)/(x+y)+1/(x2/3-x1/3*y1/3+y2/3)
- n*((1+p)^k+p^k*log(p)+(1+p)^k*(k+1)*log(1+p))/k-n*(p^k+(k+1)*(1+p)^k)/k^2
- Factor squared:
- -q^4-4*q^2+5
- -9*p^2-5*p-4
- 8*x^4-14*x^2-3
- x^2-x*a+4*a^2
- How do you in partial fractions?:
- (6x^2+29x)/(x+5)
- 3*x^2/(8-x^4)+4*x^6/(8-x^4)^2
- (x^3+12*x)*(x/(2*(x^3+12*x))+(-12-3*x^2)*(x^2+4)/(4*(x^3+12*x)^2))/(x^2+4)
- 1/(n*(n+1)*(n+2))
-
Identical expressions
- factorial(n)/factorial(n+ one)-(n- one)/factorial(n)
- factorial(n) divide by factorial(n plus 1) minus (n minus 1) divide by factorial(n)
- factorial(n) divide by factorial(n plus one) minus (n minus one) divide by factorial(n)
- factorialn/factorialn+1-n-1/factorialn
- factorial(n) divide by factorial(n+1)-(n-1) divide by factorial(n)
-
Similar expressions
- factorial(n)/factorial(n+1)+(n-1)/factorial(n)
- factorial(n)/factorial(n-1)-(n-1)/factorial(n)
- factorial(n)/factorial(n+1)-(n+1)/factorial(n)
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Expressions with functions
- factorial
- factorial(5)/(m*(m+1))*factorial(m+1)/factorial(m-1)
- factorial(n/2*(n-1))/(factorial(n-1)*factorial((n-1)*(n-2)/2))
- factorial(x)*factorial(x)/factorial(x-2)/factorial(x-1)
- factorial(n)/factorial(n+1)-factorial(n-1)/factorial(n)
- factorial(s)/factorial(7)/factorial(s-7)/factorial(factorial(2*s))
- factorial
- factorial(5)/(m*(m+1))*factorial(m+1)/factorial(m-1)
- factorial(n/2*(n-1))/(factorial(n-1)*factorial((n-1)*(n-2)/2))
- factorial(x)*factorial(x)/factorial(x-2)/factorial(x-1)
- factorial(n)/factorial(n+1)-factorial(n-1)/factorial(n)
- factorial(s)/factorial(7)/factorial(s-7)/factorial(factorial(2*s))
- factorial
- factorial(5)/(m*(m+1))*factorial(m+1)/factorial(m-1)
- factorial(n/2*(n-1))/(factorial(n-1)*factorial((n-1)*(n-2)/2))
- factorial(x)*factorial(x)/factorial(x-2)/factorial(x-1)
- factorial(n)/factorial(n+1)-factorial(n-1)/factorial(n)
- factorial(s)/factorial(7)/factorial(s-7)/factorial(factorial(2*s))
Least common denominator factorial(n)/factorial(n+1)-(n-1)/factorial(n)
The solution
You have entered
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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)
Numerical answer
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factorial(n)/factorial(n + 1) - (-1.0 + n)/factorial(n)
factorial(n)/factorial(n + 1) - (-1.0 + n)/factorial(n)
Rational denominator
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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
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/ 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
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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
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-(-Gamma(n) + n*Gamma(1 + n) - Gamma(n)*Gamma(1 + n))
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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
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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))