If x is not 0, -1, -2 or -3, then (1 + 1/x)(1 + 1/x + 1)(1 + 1/x + 2)

Question

If x is not 0, -1, -2 or -3, then  (1 + \frac{1}{x})(1 + \frac{1}{x + 1})(1 + \frac{1}{x + 2})(1 + \frac{1}{x +3})=  ?

(A)  1 + \frac{1}{x + 4}

(B)  x + 4

(C)  \frac{1}{x}

(D)  \frac{x+4}{x}

(E)  \frac{x+1}{x}

Catman · Answer

On Expanding the expression

(X+1/X)*(X+2/X+1)*(X+3/X+2)*(X+4/X+3).

On solving only (X+4)/X will remain.

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sj296 · Answer

Solve the equations or alternatively choose any value of x and check the options.

karanbishti · Answer

on expanding the equation all the variables will be canceled and only (x+4)/x will be left straight forward question

DrAnkita91 · Answer

Hi
I also got the answer as option D
I wanted to know does this ("If x is not 0, -1, -2 or -3") have any importance in the question? or its just a distraction?

Bunuel · Answer

The condition "If x is not 0, -1, -2, or -3" is crucial as it ensures that the denominators of the fractions in the question, such as 1/x, 1/(x+1), 1/(x+2), and 1/(x+3), are non-zero, ensuring that the expressions remain defined throughout the problem.

DrAnkita91 · Answer

got it..
thank you for the clarification

If x is not 0, -1, -2 or -3, then (1 + 1/x)(1 + 1/x + 1)(1 + 1/x + 2)

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If x is not 0, -1, -2 or -3, then (1 + 1/x)(1 + 1/x + 1)(1 + 1/x + 2)

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