problem: Let $a_1,a_2,a_3,\dots$ be an arithmetic sequence. If $\frac{a_4}{a_2} = 3$, what is $\frac{a_5}{a_3}$?
solution: Let $a$ be the first term, and let $d$ be the common difference.  Then $a_n = a + (n - 1)d$ for all $n$.  In particular, $a_4 = a + 3d$ and $a_2 = a + d$, so \[\frac{a + 3d}{a + d} = 3.\]Multiplying both sides by $a + d$, we get $a + 3d = 3a + 3d$, so $a = 0$.
  
  Then \[\frac{a_5}{a_3} = \frac{a + 4d}{a + 2d} = \frac{4d}{2d} = \boxed{2}.\]