Upper bound for ratio of positive terms












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Suppose $x,y ge 0$ and $a > 1.$ Do there exist constants $c_1, c_2 in [0,infty)$ which do not depend on $x$ or $y$ such that $$frac{a + frac{x}{2y}}{a-frac{1}{2}} le c_1x + c_2y$$



Thanks in advance for your help.






real-analysis calculus algebra-precalculus statistics inequality







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    $begingroup$


    Suppose $x,y ge 0$ and $a > 1.$ Do there exist constants $c_1, c_2 in [0,infty)$ which do not depend on $x$ or $y$ such that $$frac{a + frac{x}{2y}}{a-frac{1}{2}} le c_1x + c_2y$$



    Thanks in advance for your help.






    real-analysis calculus algebra-precalculus statistics inequality







    share|cite|improve this question











    $endgroup$















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      0








      0


      0



      $begingroup$


      Suppose $x,y ge 0$ and $a > 1.$ Do there exist constants $c_1, c_2 in [0,infty)$ which do not depend on $x$ or $y$ such that $$frac{a + frac{x}{2y}}{a-frac{1}{2}} le c_1x + c_2y$$



      Thanks in advance for your help.






      real-analysis calculus algebra-precalculus statistics inequality







      share|cite|improve this question











      $endgroup$




      Suppose $x,y ge 0$ and $a > 1.$ Do there exist constants $c_1, c_2 in [0,infty)$ which do not depend on $x$ or $y$ such that $$frac{a + frac{x}{2y}}{a-frac{1}{2}} le c_1x + c_2y$$



      Thanks in advance for your help.






      real-analysis calculus algebra-precalculus statistics inequality




      real-analysis calculus algebra-precalculus statistics inequality






      share|cite|improve this question















      share|cite|improve this question













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      share|cite|improve this question








      edited Jan 14 at 21:44







      Jack Burke

















      asked Jan 14 at 21:32









      Jack BurkeJack Burke

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          Takie $x_n=frac{1}{n}$ , $y_n =frac{1}{n^2}$ and observe that's such constans cannot exist.






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            $begingroup$

            Takie $x_n=frac{1}{n}$ , $y_n =frac{1}{n^2}$ and observe that's such constans cannot exist.






            share|cite|improve this answer









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              $begingroup$

              Takie $x_n=frac{1}{n}$ , $y_n =frac{1}{n^2}$ and observe that's such constans cannot exist.






              share|cite|improve this answer









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                $begingroup$

                Takie $x_n=frac{1}{n}$ , $y_n =frac{1}{n^2}$ and observe that's such constans cannot exist.






                share|cite|improve this answer









                $endgroup$



                Takie $x_n=frac{1}{n}$ , $y_n =frac{1}{n^2}$ and observe that's such constans cannot exist.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Jan 14 at 22:15









                MotylaNogaTomkaMazuraMotylaNogaTomkaMazura

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