How do you simplify ((10ab)/(x² - y²)) / ((5a(x - y))/(3ax(x + y))?

1 Answer
May 8, 2018

(6abx)/(x-y)^2

Explanation:

Let us check which term can be simplified further:
x^2-y^2 = (x+y)(x-y)

Then we know: 1/(a/b) = 1xxb/a
so now we simplify the original expression:

((10ab)/(x^2-y^2))/((5a(x-y))/(3ax(x+y))) = (10ab)/((x+y)(x-y))xx(3ax(x+y))/(5a(x-y))

((10ab)/(x^2-y^2))/((5a(x-y))/(3ax(x+y))) = (10ab)/(cancel((x+y))(x-y))xx(3axcancel((x+y)))/(5a(x-y))

((10ab)/(x^2-y^2))/((5a(x-y))/(3ax(x+y))) = (10ab)/((x-y))xx(3ax)/(5a(x-y)

((10ab)/(x^2-y^2))/((5a(x-y))/(3ax(x+y))) = (30a^2bx)/((5a)(x-y)^2)

((10ab)/(x^2-y^2))/((5a(x-y))/(3ax(x+y))) = (30/5)xx((a^(2-1)xxbx))/(x-y)^2

((10ab)/(x^2-y^2))/((5a(x-y))/(3ax(x+y))) = (6abx)/(x-y)^2