(2xy^2+16x^2y-20xy+8) / (4xy)
just divide each term by 4xy:
y/2 + 4x - 5 + 2/(xy)
To simplify the expression (2xy^2 + 16x^2y - 20xy + 8) / (4xy), you can divide each term in the numerator by the denominator.
Step 1: Divide the first term: 2xy^2 / 4xy = (2/4) * (xy^2 / xy)
Simplify the coefficient: 2/4 = 1/2
Simplify the variables: xy^2 / xy = y^2
Step 2: Divide the second term: 16x^2y / 4xy = (16/4) * (x^2y / xy)
Simplify the coefficient: 16/4 = 4
Simplify the variables: x^2y / xy = xy
Step 3: Divide the third term: -20xy / 4xy = (-20/4) * (xy / xy)
Simplify the coefficient: -20/4 = -5
Simplify the variables: xy / xy = 1
Step 4: Divide the fourth term: 8 / 4xy = (8/4) * (1 / xy)
Simplify the coefficient: 8/4 = 2
Simplify the variables: 1 / xy = (1 / x) * (1 / y) = 1 / (xy)
Putting it all together, the simplified expression is: (1/2)y^2 + 4xy - 5 + 2 / (xy)