Faction math!! please help!

Question

anonymous · Answer

Fraction or Factoring?

anonymous · Answer

x-2 / 3x-9    divided by    x^2 + x - 6 / x^2-4x+3

anonymous · Answer

This is the question, Fraction division I suppose.

anonymous · Answer

are u looking for x

anonymous · Answer

It just says simplify your answer as much as possible

mathstudent55 · Answer

I think you mean this, correct?

$\dfrac{x - 2}{3x - 9} \div \dfrac{x^2 + x - 6}{x^2-4x+3} $

anonymous · Answer

yes mathstudent55 that's exactly how the problem looks

mathstudent55 · Answer

You are dividing fractions.
How do you divide a fraction by a fraction?

anonymous · Answer

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 · Answer

this is a question on the pretest packet

mathstudent55 · Answer

For example:

$\dfrac{5}{8} \div \dfrac{3}{7} = \dfrac{5}{8} \times \dfrac{7}{3}$

you know the part above, right?

anonymous · Answer

yes.

mathstudent55 · Answer

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 · Answer

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 · Answer

Okay I'm with you so far.

mathstudent55 · Answer

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 · Answer

Right that makes sense. So x-3 and x+3 would cancel out.

mathstudent55 · Answer

No.
Factors have to be exactly the same to cancel out.

anonymous · Answer

Oh..

mathstudent55 · Answer

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 · Answer

$=\dfrac{\color{red}{\cancel{x - 2}}}{3\color{green}{(\cancel{x - 3})}} \times \dfrac{\color{green}{(\cancel{x - 3})}(x - 1)}{(\color{red}{\cancel{x - 2}})(x + 3)}$

What is left:

$=\dfrac{x - 1}{3(x + 3)} $

anonymous · Answer

Okay.. so from there how can I simplify further?

mathstudent55 · Answer

That is the final answer.

mathstudent55 · Answer

You can leave it like that or like this:

$=\dfrac{x - 1}{3x + 9} $

Both forms are equally correct and acceptable.

anonymous · Answer

okay thank you very much!

mathstudent55 · Answer

You're welcome.