anonymous
  • anonymous
Faction math!! please help!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Fraction or Factoring?
anonymous
  • anonymous
x-2 / 3x-9 divided by x^2 + x - 6 / x^2-4x+3
anonymous
  • anonymous
This is the question, Fraction division I suppose.

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anonymous
  • anonymous
are u looking for x
anonymous
  • anonymous
It just says simplify your answer as much as possible
mathstudent55
  • mathstudent55
I think you mean this, correct? \(\dfrac{x - 2}{3x - 9} \div \dfrac{x^2 + x - 6}{x^2-4x+3} \)
anonymous
  • anonymous
yes mathstudent55 that's exactly how the problem looks
mathstudent55
  • mathstudent55
You are dividing fractions. How do you divide a fraction by a fraction?
anonymous
  • anonymous
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...)
anonymous
  • anonymous
this is a question on the pretest packet
mathstudent55
  • mathstudent55
For example: \(\dfrac{5}{8} \div \dfrac{3}{7} = \dfrac{5}{8} \times \dfrac{7}{3}\) you know the part above, right?
anonymous
  • anonymous
yes.
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
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?
anonymous
  • anonymous
Okay I'm with you so far.
mathstudent55
  • mathstudent55
Now we need to factor all numerators and denominators, and see what cancels out. \(=\dfrac{x - 2}{3(x - 3)} \times \dfrac{(x - 3)(x - 1)}{(x - 2)(x + 3)} \)
anonymous
  • anonymous
Right that makes sense. So x-3 and x+3 would cancel out.
mathstudent55
  • mathstudent55
No. Factors have to be exactly the same to cancel out.
anonymous
  • anonymous
Oh..
mathstudent55
  • mathstudent55
Notice the smae color means it can be canceled: \(=\dfrac{\color{red}{x - 2}}{3\color{green}{(x - 3)}} \times \dfrac{\color{green}{(x - 3)}(x - 1)}{(\color{red}{x - 2})(x + 3)}\)
mathstudent55
  • mathstudent55
\(=\dfrac{\color{red}{\cancel{x - 2}}}{3\color{green}{(\cancel{x - 3})}} \times \dfrac{\color{green}{(\cancel{x - 3})}(x - 1)}{(\color{red}{\cancel{x - 2}})(x + 3)}\) What is left: \(=\dfrac{x - 1}{3(x + 3)} \)
anonymous
  • anonymous
Okay.. so from there how can I simplify further?
mathstudent55
  • mathstudent55
That is the final answer.
mathstudent55
  • mathstudent55
You can leave it like that or like this: \(=\dfrac{x - 1}{3x + 9} \) Both forms are equally correct and acceptable.
anonymous
  • anonymous
okay thank you very much!
mathstudent55
  • mathstudent55
You're welcome.

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