Question

(8x^2y^2+4xy^2-12y^2) ÷ 4xy^2

I received this problem. I was told to divide the rational expression. The problem I am having is I feel like something is missing. I only understand to divide rational expressions we take the first rational expression and multiply it by the reciprocal of the 2nd rational expression. To me, this doesn't look right, it looks like maybe simplify? Or how would you divide this?
Thanks.. Steph

Answer 1

Well, since this is a fairly straightforward expression, just divide each term of the numerator by the denominator. Just as in

(20+30+50)/10 = 20/10 + 30/10 + 50/10, you have

(8x^2y^2+4xy^2-12y^2) ÷ 4xy^2
= 8x^2y^2/4xy^2 + 4xy^2/4xy^2 - 12y^2/4xy^2
= 2x + 1 - 3/x

or, if you like, you can factor the numerator first and you have

4y^2(2x^2+x-3)/4xy^2
= (2x+3)(x-1)/x