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P19 [Algebra] - Turkish NMO 1st Round - 2014

Source:

May 23, 2014

Problem Statement

What is the largest possible value of x2+2x+6x2+x+5\dfrac{x^2+2x+6}{x^2+x+5} where xx is a positive real number?
<spanclass=′latex−bold′>(A)</span> 1411<spanclass=′latex−bold′>(B)</span> 97<spanclass=′latex−bold′>(C)</span> 1310<spanclass=′latex−bold′>(D)</span> 43<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ \dfrac{14}{11} \qquad<span class='latex-bold'>(B)</span>\ \dfrac{9}{7} \qquad<span class='latex-bold'>(C)</span>\ \dfrac{13}{10} \qquad<span class='latex-bold'>(D)</span>\ \dfrac{4}{3} \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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