Copying the problem:
5 4
--------- - ---------
3x^2y 6xy^3
1) Multiplying numerator and denominator of the first fraction by 2 results in:
2(5)
---------- (Call this A)
6x^2*y
2) Mult. the numerator and denom of the 2nd fraction by x results in
4x
------------- (Call this B)
6x^2y^3 and this denom. is almost the same as that of the 1st fract.
3) Mult. the num. and den. of fract. A by y^2 results in
2(5)(y^2)
--------------- (Call this C)
6x^2*y^3
Now the denominators of the 2 fractions are identical, and so we can combine them:
4x 10y^2 4x - 10y^2
------------ - -------------- = ---------------- (answer)
6x^2*y^3 6x^2*y^3 6x^2*y^3