Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2007 Cyprus MO/Lyceum/Problem 8

Revision as of 13:11, 6 May 2007 by I_like_pie (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2007_Cyprus_MO/Lyceum/Problem_8&oldid=14863"