## anonymous one year ago More help on algebra please?

1. anonymous

Rationalize the denominator and simplify $\frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}+2 }$ Once again I know I need to multiply it by the conjugate but again I need help doing the actual math. I multiplied it by $\frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}-2 }$ and I got $\frac{ 1-\sqrt{a+1} }{ -1 }$ but it doesn't fit where I need to put the answer.

2. UsukiDoll

sigh it's nice to know that someone is doing latex.. it sucks that my fraction latex is broken .

3. anonymous

latex?

4. UsukiDoll

$\frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}+2 } \cdot \frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}-2 }$

5. UsukiDoll

yeah that's used to type Math. It's called Latex. But on my end it's coo coo

6. anonymous

Ohh

7. UsukiDoll

$\frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}+2 } \cdot \frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}-2 } \rightarrow \frac{(\sqrt{a+1}-2)(\sqrt{a+1}-2)}{(\sqrt{a+1}+2)(\sqrt{a+1}-2)}$

8. UsukiDoll

can we not give direct answers please? It's against code of conduct

9. LilyMQ

oh sorry I'm new here

10. LilyMQ

deleted

11. UsukiDoll

ah. I see. Ok.

12. anonymous

@LilyMQ I do need to know how

13. UsukiDoll

14. UsukiDoll

anyway where was I? $\frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}+2 } \cdot \frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}-2 } \rightarrow \frac{(\sqrt{a+1}-2)(\sqrt{a+1}-2)}{(\sqrt{a+1}+2)(\sqrt{a+1}-2)}$

15. UsukiDoll

so we need to use the foil method... as usual the denominator is always easier because the middle terms are cut out

16. UsukiDoll

$\frac{(\sqrt{a+1}-2)(\sqrt{a+1}-2)}{(\sqrt{a+1}+2)(\sqrt{a+1}-2)} =\frac{?}{(a+1)-4}$

17. UsukiDoll

so foil is needed on the numerator .

18. UsukiDoll

our denominator should be a+1-4=a-3

19. UsukiDoll

dear gawd latex... U SUCK! |dw:1437556072647:dw|

20. anonymous

Ok I'm following

21. UsukiDoll

so now all we need to do is apply foil method to the numerator $\frac{(\sqrt{a+1}-2)(\sqrt{a+1}-2)}{(\sqrt{a+1}+2)(\sqrt{a+1}-2)} =\frac{?}{a-3}$ so foil is first outer inner last $\ \frac{\sqrt{a+1} \sqrt{a+1}-2 \sqrt{a+1}-2 \sqrt{a-1}+(-2)(-2)}{a-3}$

22. UsukiDoll

-_-

23. anonymous

It actually looks fine on my side

24. Jhannybean

Yeah same here |dw:1437556324233:dw|

25. anonymous

Ok so we end up with $a+1-2\sqrt{a+1}-2\sqrt{a+1}+4$ but I'm not sure?

26. Jhannybean

Remember your polynomial expansion : $$(a-b)^2 = a^2 -2ab+b^2$$

27. Jhannybean

And take $$a= \sqrt{a+1}$$ and $$b = -2$$

28. UsukiDoll

well a square root times a square root will just be that result so in that case it's just a+1 then (-2)(-2) is 4 you can combine the middle terms

29. anonymous

Not sure how to combine the middle terms but I know they are both $-2\sqrt{a+1}$

30. UsukiDoll

$a+1-2\sqrt{a+1}-2\sqrt{a+1}+4$ yes they both have negative signs ... factor out the square root a+1 and then do -2-2

31. UsukiDoll

yeah ...we're supposed to have -4\sqrt{a+1}

32. UsukiDoll

I would ignore the a+1 in the square root part and just compute -2-2

33. Jhannybean

$-2ab \rightarrow -2(\sqrt{a+1})(2)$ in correctingmy error.

34. anonymous

OK so I got the final answer and I figured out my error the first time and as usual it was just a simple math slip. The final answer is $\frac{ 5+a-4\sqrt{a+1} }{ a-3 }$

35. Jhannybean

That looks correct

36. anonymous

Oh my gosh wow it took me a long time but I got 100% XD

37. UsukiDoll

$a+1-2\sqrt{a+1}-2\sqrt{a+1}+4 \rightarrow \frac{a-4\sqrt{a+1}+5}{a-3}$

38. anonymous

Thanks

39. UsukiDoll

yup it's correct XD

40. anonymous

I'm still way behind on summer school but oh well lol

41. UsukiDoll

ouch. how much more material do you have to complete?

42. anonymous

I'm three percent done and I need to be 100% by August 1 XD

43. anonymous

Plus I need to be 100% done on another class too by that time

44. anonymous

So it's gonna be crunch time XD

45. UsukiDoll

oh. time for all nighters. Drink tons of coffee!

46. anonymous

Yup

47. UsukiDoll

Hmm if you complete 20% of the material, you'll get it done in 5 days XD! So that makes it July 26.

48. anonymous

Good plan I'll just get 20% done a day and I'll be done just on time XD