divide and simplify the result using formula

Question

Divide the following: 2(x+5)/(3x-9)÷3(2x+6)/((4x-20) ) , and simplify the result by using the formula: a^2-b^2=(a+b)(a-b)

Answer 1

 

When dividing fractions, KFC: keep, flip, change

 

2(x+5)      4(x-5)

--------  * -------------

3(x-3)        6(x+3)

 

 

8(x+5)(x-5)

--------------

18(x-3)(x+3)

 

which can be written

 

8(x^-25)

----------

18(x^2-9)

 

Reducing:

 

 

4(x^-25)
----------
9(x^2-9)

 

is the final answer provided that x is NOT 3 nor -3