## anonymous 5 years ago OMG i need help, I'm working on Rational expression: 7- a-2/a+3 = a(squared)-4/a+3 +5.. anyone?

1. anonymous

[7-(a-2/a+3)]=[(a^2-4)/a+3)+5] right?

2. anonymous

is it:$7 - \frac{a-2}{a+3} = \frac{a^2-4}{a+3} + 5$?

3. anonymous

sstarica how you write that symbols

4. anonymous

using the equation button down-left on your past box :)

5. anonymous

post*

6. anonymous

yes that is it! ok i see the equation button

7. anonymous

I did try but I can write the faction

8. anonymous

i know the answer but i have no idea how they got it im so stomped

9. anonymous

use frac{}{} for the fraction :), alright, if that's your question then the answer is the following

10. anonymous

$7+5 - \frac{(a-2)}{a+3} - \frac{(a^2-4)}{a+3} = 0$$\frac{12(a+3) - a + 2 - a^2 + 4}{a+3} = \frac{12a + 36 - a + 2 - a^2 + 4}{a+3}$$= \frac{-a^2-11a+42}{a+3} = \frac{-(a^2+11a-42)}{a+3}$$= \frac{-(a+3)(a-14)}{a+3} = -(a-14) \rightarrow -a+14$ Correct me if I'm wrong ^_^

11. anonymous

wait, it's 11 a and not -11 a ^_^" sorry

12. anonymous

humm the book has an answer of 4 only, I am confused

13. anonymous

so :$= \frac{-a^2 + 11a +42}{a+3}$$= \frac{-(a^2-11a-42)}{a-3} = \frac{-(a+3)(a-14)}{a+3}$ I just messed up the sign of 11, so in the end when you simplify you'll get -a+14, I guess

14. anonymous

4? weird

15. anonymous

a = 14 in this case?

16. anonymous

yeah, it gives x=4 only

17. anonymous

x? but we are dealing with a here

18. anonymous

im sorry a yes

19. anonymous

lol, that's weird.

20. anonymous

hang on

21. anonymous

what i did was mutliply each side by (a+3)

22. anonymous

so i ended up with

23. anonymous

I GOT IT!

24. anonymous

25. anonymous

steps:

26. anonymous

7(a+3) - a - 2 = a^{2}-4 + 5(a+3)

27. anonymous

28. anonymous

$\frac{-(a-2)}{a+3} - \frac{a^2-4}{a+3} = 5-7$$\frac{-a^2-a-6}{a+3} = -2$$\frac{-(a^2+a-6)}{a+3} = -2$$\frac{-(a-2)(a+3)}{a+3} = -2$$-(a-2) = -2 \rightarrow -a +2 = -2$$-a = -4 \rightarrow a = 4$ ^_^

29. anonymous

lol in the 2nd line it's supposed to be + 6, but just a small typo, doesn't effect the solution :)

30. anonymous

so ur first step was to subtract the entire fraction from one side?

31. anonymous

yes, I moved 7 to the other side and got all the a's in one side :) and started solving for a ^_^

32. anonymous

oh i didnt know you could do that

33. anonymous

lol, it's like solving for x: 4x -3 = x + 2, solve for x <-- move the x's in one side and numbers in one side ^_^

34. anonymous

and now since both fractions have the same denominator i can simply subtrat the entire top row

35. anonymous

yep :)

36. anonymous

wait what happend to the (a+3) how did that cancel?

37. anonymous

you simplified, cancel the (a+3) from top and bottom ^_^

38. anonymous

and you'll be left with only -(a-2) :)

39. anonymous

ok perfect, i got it, then when you divde at the end the two -1's cancel out and -4/-1 = postitive 4.. haha perfect

40. anonymous

yep ^_^

41. anonymous

next time don't panic :P and face the problem calmly ^_^ good luck!

42. anonymous

thank you, it just never crossed my mind that i could move the entire fraction, i was so worried about mutliplying every side the the LCD that i got stuck on it for an hour.. thank you!

43. anonymous

my answer: (7*(a+3))-(a-2)=(a^2-4)+(5*(a+3) (7a+21)-(a-2)=(a^2-4)+(5a+15) 6a+23=a^2+5a+11 a^2-a-12=0 Factor:(a+3)(a-4)

44. anonymous

you are most welcome ^_^, worrying = distracts you from concentrating. Look at it as simple as possible then you'll be able to solve it :)

45. anonymous

hmm, nancy lam's solution seems simple too :)

46. anonymous

nancy ur answer works too i think, its that x would = -3 which would be no solution, but the x=4 would work

47. anonymous

but I don't know write like you see better

48. anonymous

as long as the denominator isn't zero, from what i remember in class

49. anonymous

2 solution , and lug it in to see which one work

50. anonymous

i was doing it your way nancy, but somehow, i got messed up with my signs

51. anonymous

u got rid of the denominator right from the beginning which is what i was trying to do im going to work it over again and see where i messed up

52. anonymous

I working write fraction like sstarica

53. anonymous

you time (a+3) for which one don't have denominator and get rid all denominator from beginning

54. anonymous

ok, bye

55. anonymous

Thank you, both of you! now i can sleep!

56. anonymous

you wellcome

57. anonymous

np :)