how do i simplify this complex fraction?

Question

1/3 - 1/x / 2/9x - 2/3x^2 please show me the details on how you came up with your answer. :)

Answer 1

Here is the answers:
First, organise the numirator:
1/3 - 1/x = (x/x)(1/3) - (3/3)(1/x) = (x/3x) - (3/3x)
= (x-3) /3x

Now the denominator:
2/9x - 2/3(x^2) = [3(x^2) / 3(x^2)](2/9x) - (9x / 9x)[2/ 3(x^2)]
= [ 6(x^2) / 27(x^3)] - [18x / 27(x^3)] = [ 6(x^2) -18] / [ 27(x^3) ]

[ (x-3) /3x ] / { [ 6(x^2) -18] / [ 27(x^3) ] } =

[(x-3)/3x ] * { [ 27(x^3) ] / [ 6(x^2) -18] } =

(x-3)*[ 27(x^3) ] / { 3x * [ 6(x^2) -18] } =

(x-3)(3x)(3x)(3x) / { (3x)*[ 6x( x-3) ] } =

(3x)(3x)/ 6x = 9x^2 / 6x = 9x/6 = 3x/2

Answer 2

Is the fraction exactly as shown or have you omitted some brackets? If there are no brackets then the middle term
1/x/ 2/9x = 1/x multiplied by 9x/2 =9/2, so the complete expression is 1/3 - 9/2 - 2/3x^2 = -25/6 -2/3x^2. If, however, the original expression is (1/3 - 1/x)/(2/9x - 2/3x^2) then the simplified form is 3x/2. This is arrived by the method shown in the answer by MollyMAM. Leaving out brackets completely changes the problem!

Answer 3

I like multiplying the whole mess by the LCD which is 9x^2. That simplifies it to 3x^2 - 9x / 2x - 6; factoring the numerator and denominator, you get 3x(x-3) / 2(x-3). The x-3 cancels out and the answer is 3x/2.

Answer 4

if by this you mean

((1/3) - (1/x))/((2/(9x)) - (2/(3x^2))

multiply top by 3x and bottom by 9x^2

((x - 3)/(3x))/(((2x - 2(3)))/(9x^2))

((x - 3)/(3x))/(((2x - 6)/(9x^2))

((x - 3)/(3x))*((9x^2)/(2x - 6))

((9x^2)(x - 3))/((3x)(2x - 6))

(((3x)(x - 3))x)/(2((3x)(x - 3)))

(x/2)

ANS : (x/2)

Answer 5

Yeah, there's always somebody in Yahoo Answers willing to do your homework for you. Your problem is in sorting out the myriad of completely wrong answers. Frankly, I would think it more practical to figure it out for yourself.