Solve [(9x^2 - 9y^2)/(6x^2y^2)]/[(3x + 3y)/(12x^2y^5)] .

To solve

[(9x^2 - 9y^2)/(6x^2y^2)]/[(3x + 3y)/(12x^2y^5)] .

Solution:

We know (a/b)/ (c/d) = ad/(bc)

Rewriting  in numerator and denominator form we get: (9x^2-9y^2)(12x^2y^5)/ {(6x^2y^2)(3x+3y)}........(1)

Numerator = (3x+3y)(3x-3y)(1`2x^2y^5), as (a^2-b^2= (a+b)(a-b), wehre a= 3x and b= 3y and a^2-b^2 = 9x^2-9y^2.

Denominator =(3x+3y)(6x^2y^2)

Therefore reducing the expresion's ( at (1) ) numerator and denominator  (3x+3y)(6x^2y^2), the HCF of numerator and denominators:

(3x-3y)(2y^3) = 6(x-y)y^3