Question

How do you simplify `(144)/(4xy)div (54y^3)/(3x^3y)`?

Answer 1

Dividing by a fraction is the same as multiplying with the inverse.

Explanation:

So we invert the second fraction (=put it upside down):
`=144/(4xy)xx(3x^3y)/(54y^3)=(144*3x^3y)/(4*54xy*y^3)=(432x^3y)/(216xy^4)`

Then we factorize as far as necessary, and cancel:
`=(2*cancel216*cancelx*x*x*cancely)/(cancel216*cancelx*cancely*y*y*y)=(2x^2)/y^3`