Question

Can somebody explain this?

Answer 1

(xy+5)/(xy+3)

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.

`(x^2y^2-4)/(x^2y^2+xy-2)/(x^2y^2+xy-6)/(x^2y^2+4xy-5)=(x^2y^2-4)/(x^2y^2+xy-2)*(x^2y^2+4xy-5)/(x^2y^2+xy-6)\\\\=((x^2y^2-4)(x^2y^2+4xy-5))/((x^2y^2+xy-2)(x^2y^2+xy-6))=((xy-2)(xy+2)(xy-1)(xy+5))/((xy-1)(xy+2)(xy-2)(xy+3))\\\\=\boxed{(xy+5)/(xy+3)}`