2. find the lcd of the fractions, and then simplify the expression. assume that no denominator equals zero.

5/3x^2y-4/6xy^3

In looking for the LCD, we must first look for the least common multiple (LCM) of the numbers:
LCM of 3 and 6 = 6
LCM of x² and x = x²
LCM of y³ and y = y³
Therefore, the Least Common Denominator of both fractions is 6x²y³

To simply this expression:

=
= (5*2y^2) / (3x^2y*2y^2) - (4*x)/(6xy^3*x)
= (10y^2)/(6x^2y^3) - (4x)/(6x^2y^3)
= (10y^2 - 4x) / (6x^2y^3)
= (5y^2 - 2x) / (3x^2y^3)

So the simplified equation is: