Can a fraction be simplified using Anomalous Cancellation?

Pyth, 22 19 bytes

Thanks to @isaacg for three bytes!

qFcMsMM,Jcz\/.-M_BJ

Explanation:

qFcMsMM,Jcz\/.-M_BJ      Implicit: z=input().
       ,                 two-element list
        Jcz\/              J = split z on ','
                _BJ      Bifurcate reverse: [J,reversed(J)]
             .-M         map multiset difference of elements in both lists
                             this gives the multiset difference both ways
       ,Jcz\/.-M_BJ      On input 1019/5095: [['1019','5095'], ['11','55']]
    sMM                  convert all strings to numbers
  cM                     map by float division
qF                       fold equality

Try it here.

TeaScript, 22 bytes

xs`/`[0]M#E(xg(l))⌐E(x

Now that all the bugs are ironed out in TeaScript 3, this works nicely

Try it online

Test suite

, 17 chars / 34 bytes

ïČ⍘/⎖0ⓢⓈë(ïę$)≔ëï

Try it here (Firefox only).

Explanation

ïČ⍘/⎖0ⓢⓈë(ïę$)≔ëï // implicit: ï = input fraction
ïČ⍘/⎖0              // get the numerator...
      ⓢ            // split it...
        Ⓢ          // and check if any of its items satisfy the condition:
          ë(ïę$)    // When the item is removed from ï,
                ≔ëï // does its fractional value still equal the original fractional value?
                    // implicit output