SOLUTION: perform the indicated operations involving rational expressions. Express the final answer in simplest form. (6xy^2/14)(21x^3y/10y) / (10y/21x^3)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: perform the indicated operations involving rational expressions. Express the final answer in simplest form. (6xy^2/14)(21x^3y/10y) / (10y/21x^3)      Log On


   

Question 420757: perform the indicated operations involving rational expressions. Express the final answer in simplest form.
(6xy^2/14)(21x^3y/10y) / (10y/21x^3)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
First of all, while you may consider this expression to be a complex one, it does not involve "complex numbers". I have corrected the category to reflect the actual type of problem this is.

%28%286xy%5E2%29%2F14%29%28%2821x%5E3y%29%2F%2810y%29%29%2F%28%2810y%29%2F%2821x%5E3%29%29
Since fractions are another way of expressing a division, we are going to start by changing the division represented by the "big" fraction into the product of its numerator by the reciprocal of its denominator:
%28%286xy%5E2%29%2F14%29%28%2821x%5E3y%29%2F%2810y%29%29%28%2821x%5E3%29%2F%2810y%29%29
When multiplying fractions one is allowed to cancel common factors, even from one fraction across to another, before doing the actual multiplication. This is optional. But it is usually a good idea to do so.

To cancel common factors we must know what the factors are and which ones are common. You may very well be able to "see" these common factors already. But in case you can't see these factors, I am going break down each numerator and denominator into prime factors:

Now we can cancel the factors that are common to the numerators and denominators:

leaving

Now we can multiply:
%28187x%5E7y%29%2F100