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2007 Cyprus MO/Lyceum/Problem 8

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Problem

If we subtract from 2 the inverse number of x-1, we get the inverse of x-1. Then the number x+1 equals to

\mathrm{(A) \ } 0\qquad \mathrm{(B) \ } 1\qquad \mathrm{(C) \ } -1\qquad \mathrm{(D) \ } 3\qquad \mathrm{(E) \ } \frac{1}{2}

Solution

2-\frac1{x-1}=\frac1{x-1}


2=\frac2{x-1}

Multiplying out and solving, we get that x = 2, so x+1=3\Longrightarrow\mathrm{ D}.

See also

2007 Cyprus MO, Lyceum (Problems)
Preceded by
Problem 7 		Followed by
Problem 9
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
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