The solution of (1+1/x) (1+1/x+1) (1+1/x+2) (1 + 1/x + 3) is?
- x + 6/x
- x + 8/x
- x + 4/x
- None of these
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
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