Answer:
(xy+5)/(xy+3)
Step-by-step explanation:
Given a ratio of rational expressions, you want the simplified version.
Simplifying
The colon separating the two expressions is one of the ways a ratio is written. In this context, it can be replaced by "divided by" (÷). Of course, the division is carried out in the usual way: multiplying by the inverse of the denominator.
The product is simplified by cancelling common factors. This requires each of the polynomials be factored.
[tex]\dfrac{x^2y^2-4}{x^2y^2+xy-2}\div\dfrac{x^2y^2+xy-6}{x^2y^2+4xy-5}=\dfrac{x^2y^2-4}{x^2y^2+xy-2}\times\dfrac{x^2y^2+4xy-5}{x^2y^2+xy-6}\\\\=\dfrac{(x^2y^2-4)(x^2y^2+4xy-5)}{(x^2y^2+xy-2)(x^2y^2+xy-6)}=\dfrac{(xy-2)(xy+2)(xy-1)(xy+5)}{(xy-1)(xy+2)(xy-2)(xy+3)}\\\\=\boxed{\dfrac{xy+5}{xy+3}}[/tex]
