## anonymous one year ago How to simplify this?? $\frac{-\sqrt{3} - 1}{1+(-\sqrt{3})*1}$ $\frac{-\sqrt{3} - 1}{1-\sqrt{3}}$ $\frac{-\sqrt{3} - 1}{1-\sqrt{3}} * \frac{1-\sqrt{3}} {1-\sqrt{3}}$ $\frac{2}{2(2-\sqrt{3})}$ Is this correct??

1. anonymous

In step 3, you should multiply the expression by the denominator's conjugate, top and bottom.

2. anonymous

That allows you to eliminate radical expressions in the denominator.

3. anonymous

Could you show me? I don't see what you mean. I thought I did multiply the expression

4. anonymous

$\frac{ -\sqrt{3}-1 }{ 1-\sqrt{3} } \times \frac{ 1+\sqrt{3} }{ 1+\sqrt{3} }$

5. anonymous

That should be your step 3.

6. anonymous

I did that and I get 2 for the numerator and $$2(2-\sqrt{3})$$ for the denominator

7. anonymous

No, if you multiply a radical expression by its conjugate, the square roots disappear.

8. anonymous

Yeah, I used the same I see that.

9. anonymous

I use - and not the conjugate

10. anonymous

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

11. anonymous

Do you agree with my above expansion?

12. anonymous

Yes

13. anonymous

Ok, so 2 is now your denominator.

14. anonymous

Let me do the top

15. anonymous

Let's multiply the numerator now.

16. anonymous

I got -2

17. anonymous

One sec I made a boo boo

18. anonymous

Check your numerator again. It should contain some square roots.

19. anonymous

I have $-\sqrt{3} -\sqrt{9} -1 -\sqrt{3}$ is this correct?

20. anonymous

Yes, you can combine the terms to make it easier to read.

21. anonymous

$-2\sqrt{3}-4$

22. anonymous

Now that you have the numerator, don't forget that you still have a denominator, -2.

23. anonymous

From what I put up where di the 4 come from?

24. anonymous

Oh your $- \sqrt{9} - 1 = -3 - 1 = - 4$

25. anonymous

26. anonymous

Ok how about eh 2 and the sqr(3) ?? from what I put up.

27. anonymous

Oh that's from $-\sqrt{3}-\sqrt{3} = -2\sqrt{3}$

28. anonymous

$\frac{ -2\sqrt{3}-4 }{ -2 } = \sqrt{3} + 2$

29. anonymous

Yep that is it. Thank you so much.

30. anonymous

Are you a qualified helper?

31. anonymous

I just like to help :)