Explanation

(1+1/x) (1+1/x+1) (1+1/x+2) (1 + 1/x + 3)

Simplify each term:

(x+1)/x * (x+2)/x * (x+3)/x * (x+4)/x

Multiply the numerators and denominators:

(x+1)(x+2)(x+3)(x+4) / x^4

Expand the numerator:

x^4 + 10x^3 + 35x^2 + 50x + 24

Divide by x^4:

1 + 10/x + 35/x^2 + 50/x^3 + 24/x^4

Now, simplify the expression:

Combine like terms:

x + 4/x