QA – Placement Quizzes | Algebra | Question 11

If 2x/(1 + 1/(1 + x/(1 – x))) = 1, then find the value of x.
(A) 1/3
(B) 2/3
(C) 1/2
(D) 3/2


Answer: (B)

Explanation: We have
2x/(1 + 1/(1 + x/(1-x))) = 1
2x/(1 + 1/((1-x+x)/(1-x))) = 1
2x/(1 + 1/(1/(1-x))) = 1
2x/(1 + 1-x) = 1
2x/(2-x) = 1
2x = 2-x
3x = 2
x = 2/3.

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