Sr Examen
¿Cómo vas a descomponer esta (5!/m(m+1))*(m+1)/(m-1)!*3! expresión en fracciones?
Solución
Ha introducido
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5!
--*(m + 1)*(m + 1)
m
------------------*3!
(m - 1)!
$$\frac{\frac{5!}{m} \left(m + 1\right) \left(m + 1\right)}{\left(m - 1\right)!} 3!$$
((((factorial(5)/m)*(m + 1))*(m + 1))/factorial(m - 1))*factorial(3)
Simplificación general
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2 720*(1 + m) ------------ Gamma(1 + m)
$$\frac{720 \left(m + 1\right)^{2}}{\Gamma\left(m + 1\right)}$$
720*(1 + m)^2/gamma(1 + m)
Respuesta numérica
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720.0*(1.0 + m)^2/(m*factorial(m - 1))
720.0*(1.0 + m)^2/(m*factorial(m - 1))
Unión de expresiones racionales
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2 720*(1 + m) ------------ m*(-1 + m)!
$$\frac{720 \left(m + 1\right)^{2}}{m \left(m - 1\right)!}$$
720*(1 + m)^2/(m*factorial(-1 + m))
Potencias
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2 720*(1 + m) ------------ m*(-1 + m)!
$$\frac{720 \left(m + 1\right)^{2}}{m \left(m - 1\right)!}$$
6*(1 + m)*(120 + 120*m)
-----------------------
m*(-1 + m)!
$$\frac{6 \left(m + 1\right) \left(120 m + 120\right)}{m \left(m - 1\right)!}$$
6*(1 + m)*(120 + 120*m)/(m*factorial(-1 + m))
Combinatoria
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2 720*(1 + m) ------------ Gamma(1 + m)
$$\frac{720 \left(m + 1\right)^{2}}{\Gamma\left(m + 1\right)}$$
720*(1 + m)^2/gamma(1 + m)
Denominador común
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2
3!*5! + m *3!*5! + 2*m*3!*5!
----------------------------
m*(-1 + m)!
$$\frac{m^{2} \cdot 3! 5! + 2 m 3! 5! + 3! 5!}{m \left(m - 1\right)!}$$
(factorial(3)*factorial(5) + m^2*factorial(3)*factorial(5) + 2*m*factorial(3)*factorial(5))/(m*factorial(-1 + m))
Compilar la expresión
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2 (1 + m) *3!*5! -------------- m*(m - 1)!
$$\frac{\left(m + 1\right)^{2} \cdot 3! 5!}{m \left(m - 1\right)!}$$
(1 + m)^2*factorial(3)*factorial(5)/(m*factorial(m - 1))
Denominador racional
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2 720*(1 + m) ------------ m*(-1 + m)!
$$\frac{720 \left(m + 1\right)^{2}}{m \left(m - 1\right)!}$$
720*(1 + m)^2/(m*factorial(-1 + m))
Parte trigonométrica
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2 720*(1 + m) ------------ m*(-1 + m)!
$$\frac{720 \left(m + 1\right)^{2}}{m \left(m - 1\right)!}$$
720*(1 + m)^2/(m*factorial(-1 + m))