Having a nightmare with fraction manipulation, here is an easy and natural solution for doing it.
Let us take,
3 4
--- + ---- = Multiply Crosswise and add ( 3 X 6 = 18 and 5 X 4 = 20,
5 6 that makes 18 + 20 = 38).
( In Maths terms Multiply Left Numerator By Right Denominator and vice verse)
So Top of the answer is : 38 (Numerator)
For calculating bottom of the answer simply multiply both the numbers in bottom (5 X 6= 30). (Denominator)
So the answer is 38
------
30.
If you want to subtract ? instead of adding both numbers to figure out the top of the answer (Numerator), just subtract.
Isn't simple enough ?

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