Faction math!! please help!

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Faction math!! please help!

Mathematics
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Fraction or Factoring?
x-2 / 3x-9 divided by x^2 + x - 6 / x^2-4x+3
This is the question, Fraction division I suppose.

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are u looking for x
It just says simplify your answer as much as possible
I think you mean this, correct? \(\dfrac{x - 2}{3x - 9} \div \dfrac{x^2 + x - 6}{x^2-4x+3} \)
yes mathstudent55 that's exactly how the problem looks
You are dividing fractions. How do you divide a fraction by a fraction?
Sort of but I'm taking a test and I havent seen the stuff in years (it's a final exam that I never took like 3 years ago and now I need it to graduate -.- so I have to take it and pass...)
this is a question on the pretest packet
For example: \(\dfrac{5}{8} \div \dfrac{3}{7} = \dfrac{5}{8} \times \dfrac{7}{3}\) you know the part above, right?
yes.
To divide a fraction by a fraction, multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is just flipping the fraction.
That means with our problem we can do that step, the flipping of the second fraction. \(=\dfrac{x - 2}{3x - 9} \times \dfrac{x^2-4x+3}{x^2 + x - 6} \) Ok so far?
Okay I'm with you so far.
Now we need to factor all numerators and denominators, and see what cancels out. \(=\dfrac{x - 2}{3(x - 3)} \times \dfrac{(x - 3)(x - 1)}{(x - 2)(x + 3)} \)
Right that makes sense. So x-3 and x+3 would cancel out.
No. Factors have to be exactly the same to cancel out.
Oh..
Notice the smae color means it can be canceled: \(=\dfrac{\color{red}{x - 2}}{3\color{green}{(x - 3)}} \times \dfrac{\color{green}{(x - 3)}(x - 1)}{(\color{red}{x - 2})(x + 3)}\)
\(=\dfrac{\color{red}{\cancel{x - 2}}}{3\color{green}{(\cancel{x - 3})}} \times \dfrac{\color{green}{(\cancel{x - 3})}(x - 1)}{(\color{red}{\cancel{x - 2}})(x + 3)}\) What is left: \(=\dfrac{x - 1}{3(x + 3)} \)
Okay.. so from there how can I simplify further?
That is the final answer.
You can leave it like that or like this: \(=\dfrac{x - 1}{3x + 9} \) Both forms are equally correct and acceptable.
okay thank you very much!
You're welcome.

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