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2007 Cyprus MO/Lyceum/Problem 8

Revision as of 12:11, 6 May 2007 by I_like_pie (talk | contribs)
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Problem

If we substract 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

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

$2=\frac2{x-1}$

$2x-2=2$

$2x=4$

$x=2$

$x+1=3\Rightarrow\mathrm{ D}$

See also

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