## amonoconnor one year ago How do you simply the following expression: (((sqrt(6-x))-2)/((sqrt(3-x)-1)))*(((sqrt(3-x))+1)/((sqrt(3-x))+1))) Thank you very much! Any and all help is greatly appreciated!

1. Mertsj

$\frac{\sqrt{6-x}-2}{\sqrt{3-x}-1}\times \frac{\sqrt{3-x}+1}{\sqrt{3-x}+1}$

2. Mertsj

Is that the problem?

3. amonoconnor

Yes!

4. Mertsj

In the denominator of the first fraction: is it -1or +1

5. jackthegreatest

well for one u can cross out the equation on the right, the top and bottom r exactly the same

6. amonoconnor

Shoot.. you are correct. "-1"

7. Mertsj

If the problem is as I have posted it the denominators are of the form (a-b)(a+b) and that is equal to a^2-b^2

8. amonoconnor

I know, that's the point: Multiplying by the conjugate, but I'm weary as to how to multiple that across... ?

9. Mertsj

So the denominator is 3-x-1or 2-x

10. Mertsj

now let's do the numerator multiplication:

11. amonoconnor

How did you get that? :/ I'm not disagreeing, I just don't know how you worked it out..

12. Mertsj

$(\sqrt{6-x}-2)(\sqrt{3-x}+1)=\sqrt{(6-x)(3-x)}+\sqrt{6-x}-2\sqrt{3-x}-2$

13. Mertsj

What is (a-b)(a+b)

14. amonoconnor

(18 - 9x + x) :)

15. Mertsj

Where did that come from?

16. amonoconnor

Isn't that what'll be under the radical, in the first term in the numerator? :/

17. Mertsj

It would be 18-9x+x^2

18. amonoconnor

Dude, I'm tired.. my bad again.

19. Mertsj

so put that numerator over 2-x and you are done.

20. amonoconnor

Can we cancel out anything else?

21. Mertsj

Are there any common factors?

22. amonoconnor

|dw:1442976045683:dw|

23. amonoconnor

Is this all correct, and the final version?

24. Mertsj

yep

25. amonoconnor

|dw:1442976240464:dw|

26. amonoconnor

This is totally wrong, right?

27. Mertsj

it is correct.

28. amonoconnor

The second version is correct as well??

29. amonoconnor

That was my initial, instinctual way to multiple the numerator across, but I thought for sure it was wrong, and I understand how you first showed me, foiling the polynomials UNDER the radical, getting 18 - 9x + x^2. But are you saying that my instinctual way works?