Evaluate the product (x+x/y)*(x-x/y) for x=30 and y=15

We notice that the product could be transformed into a
difference of squares:

(x+x/y)*(x-x/y) = x^2 -
(x/y)^2

x^2 - (x/y)^2 = x^2 -
x^2/y^2

We'll factorize by
x^2:

x^2 - x^2/y^2 = x^2*(1 -
1/y^2)

Now, we'll substitute x and y into the given
expression:

x^2*(1 - 1/y^2) = 900*(1 -
1/225)

We'll re-write the
expression:

900*(1 - 1/225) =
900(225-1)/225

900*(1 - 1/225) =
900*224/225

900*(1 - 1/225) =
4*224

900*(1 - 1/225) = 896

We
also could write the difference of squares, 25 - 1, as:

225
- 1 = (15-1)(15+1) = 14*16

(x+x/y)*(x-x/y) =
896