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## anonymous one year ago Faction math!! please help!

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1. anonymous

Fraction or Factoring?

2. anonymous

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

3. anonymous

This is the question, Fraction division I suppose.

4. anonymous

are u looking for x

5. anonymous

It just says simplify your answer as much as possible

6. mathstudent55

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

7. anonymous

yes mathstudent55 that's exactly how the problem looks

8. mathstudent55

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

9. 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...)

10. anonymous

this is a question on the pretest packet

11. mathstudent55

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

12. anonymous

yes.

13. 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.

14. 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?

15. anonymous

Okay I'm with you so far.

16. mathstudent55

Now we need to factor all numerators and denominators, and see what cancels out. $$=\dfrac{x - 2}{3(x - 3)} \times \dfrac{(x - 3)(x - 1)}{(x - 2)(x + 3)}$$

17. anonymous

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

18. mathstudent55

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

19. anonymous

Oh..

20. mathstudent55

Notice the smae color means it can be canceled: $$=\dfrac{\color{red}{x - 2}}{3\color{green}{(x - 3)}} \times \dfrac{\color{green}{(x - 3)}(x - 1)}{(\color{red}{x - 2})(x + 3)}$$

21. 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: $$=\dfrac{x - 1}{3(x + 3)}$$

22. anonymous

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

23. mathstudent55

That is the final answer.

24. mathstudent55

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

25. anonymous

okay thank you very much!

26. mathstudent55

You're welcome.

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