(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
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
To divide the rational expression (8x^2y^2+4xy^2-12y^2) ÷ 4xy^2, you need to simplify the expression by canceling out common factors and dividing each term by the given divisor one at a time.
Here's how you can divide the given expression step by step:
Step 1: Factor out the common factor, if any.
In this case, we can factor out 4y^2 from each term:
4y^2(2x^2 + xy - 3)
Step 2: Divide each term by the divisor, 4xy^2.
Divide each term of the factored expression by 4xy^2:
(2x^2 + xy - 3) ÷ (xy^2)
Step 3: Simplify further if possible.
Since there are no common factors that can be canceled out between the numerator and the denominator, the expression cannot be simplified any further.
Hence, the division of the rational expression (8x^2y^2+4xy^2-12y^2) ÷ 4xy^2 simplifies to (2x^2 + xy - 3) ÷ (xy^2).