((7x-3)/(14x^2-69x+27))/((6x^2)/(18x-81)) Simplify This Expression.

I have this problem on my homework and i cannot seem to figure it out. The answer i got is: 9/6x^2

7x - 3.............................6x^2
______________ ÷ _____________; factor the denominators
14x^2 - 69x + 27............18x - 81

7x - 3...........................6x^2
____________ ÷ _______________; cancel common terms
(7x - 3)(2x - 9).............9(2x - 9)

1...........................6x^2
_______ ÷ ________________; flip the second fraction and use multiplication
(2x - 9)..............9(2x - 9)

1.....................9(2x - 9)
______ * _______________; combine into one fraction
2x - 9................6x^2

1 * 9(2x - 9)
___________; multiply
(2x - 9)(6x^2)

1(18x - 81)
___________; simplify the numerator
12x^3 - 54x^2

18x - 81
____________; factor numerator and denominator
12x^3 - 54x^2

9(2x - 9)
___________; cancel common terms
6x^2(2x - 9)

9
____; reduce by 3
6x^2

3
___ <-----------------Answer
2x^2


Blessings

(7x-3) / (14x^2-69x+27) DIVIDED BY 6x^2 / (18x-81)

fully factor everything

(7x-3) / (7x-3)(2x-9) DIVIDED BY 6x^2 / 9(2x-9)

NOTE that (7x-3) / (7x-3) = 1

1 / 1(2x-9) DIVIDED BY 6x^2 / 9(2x-9)

which is the same as

1 / (2x-9) TIMES 9(2x-9) / 6x^2

NOTE that (2x-9)s cross-cancel each other out, leaving you with

1 / 1 TIMES 9 / 6x^2

NOTE that 3 goes into 9 thrice and into 6 twice

1/1 TIMES 3 / 2x^2

3 / 2x^2

can't simplify further

you're correct, 9/6x^2 is the right answer

top simplified is1/(2x-9)
have to show the rest if you need it solved