November 13th, 2017, 08:03 AM  #1 
Senior Member Joined: May 2014 From: Allentown PA USA Posts: 101 Thanks: 6 Math Focus: dynamical systen theory  Concerning infinity as a limit
Dear MyMathForum Community: This is the problem: as x > infinity, (2x+3)/(5x+7) = 2/5. Why is this so? Thank you. 
November 13th, 2017, 08:22 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,031 Thanks: 2342 Math Focus: Mainly analysis and algebra 
\begin{align*}\frac {2x+3}{5x+7}&= \frac{\frac25(5x+7)+\frac15}{5x+7} \\ &= \frac25 \cdot \frac{5x+7}{5x+7} +\frac15 \cdot \frac1{5x+7} \\ &= \frac25 +\frac1{5(5x+7)} \end{align*} An easier way to get the same result is $$\frac {2x+3}{5x+7} = \frac{2 + \frac3{x}}{5+\frac7{x}}$$ Last edited by v8archie; November 13th, 2017 at 08:28 AM. 

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