1. anonymous

2. anonymous

$X>7 or -2<X<6 or X \le-3$

3. anonymous

that's the answer, and I don't understand how to do that!

4. anonymous

5. anonymous

factorize the top and the bottom separately first

6. anonymous

you mean =0?

7. anonymous

yes

8. anonymous

so we get (x+3)((x-6) for the nominator

9. anonymous

and for the denominator we get (x-7)(x+2)

10. anonymous

ok, now, what values of x cannot work

11. anonymous

$\frac{ (x-6)(x+3) }{ (x-7)(x+2) }$

12. anonymous

7 and 2

13. anonymous

right?

14. anonymous

but how from here?

15. anonymous

can you please show how to calculate from here?

16. anonymous

@Emeyluv99

17. anonymous

sorru. computers being mean.. and be careful, its 7 and -2

18. anonymous

now the way I would do it, graph the quadratic you get in the numerator. See what values of x give a positive y and that's you're answer. Be careful to exclude 7 and -2 though

19. anonymous

that's what I did but I didn't get the asnswer

20. anonymous

from graphing you should get x<-3 and x>6... but, since we can't have 7 you should get X<-3, 6<x<7, and x>7

21. anonymous

but that's not the answer... thanks though

22. anonymous

@ganeshie8 will you be savior?

23. anonymous

my

24. ganeshie8

|dw:1440157290238:dw|

25. ganeshie8

pick any number to the left of -3 say -4 plug x = -4 in the given inequality

26. ganeshie8

$\frac{ (x-6)(x+3) }{ (x-7)(x+2)}$ plugging x=-4 gives $\frac{ (-4-6)(-4+3) }{ (-4-7)(-4+2) }$ looks it is positive, yes ?

27. anonymous

yes

28. anonymous

but why would you put -4 from the first place?

29. anonymous

?

30. ganeshie8

you can put any number to the left of -3 for testing since -4 is easy to work..

31. anonymous

oh ok, then what am I doing from here?

32. ganeshie8

since a number to the left of -3 satisfies the inequality, $$x\lt 3$$ is part of the solution : |dw:1440158449273:dw|

33. ganeshie8

lets check the next interval $$(-3, -2)$$ pick a number between -3 and -2

34. ganeshie8

thr ? @Hipocampus

35. anonymous

-2.5

36. anonymous

sorry there's a slightly problem with the internet

37. anonymous

sorry I'm not following thanks though

38. anonymous

it's supposed to be a really easy question

39. ganeshie8

$\frac{ (x-6)(x+3) }{ (x-7)(x+2)}$ plugging x=-2.5 gives $\frac{ (-2.5-6)(-2.5+3) }{ (-2.5-7)(-2.5+2) }$ looks it is negative, yes ?

40. anonymous

yes

41. ganeshie8

so the interval (-3, -2) is not a solution : |dw:1440159462256:dw|

42. ganeshie8

to test the next interval $$(-2,6)$$ pick some easy number between them and plug it in the inequality

43. anonymous

so I need to plug in 4 times?

44. anonymous

can we try -1.5 together please? I think I've got it!

45. ganeshie8

try some easy number like x=0

46. ganeshie8

0 is between -2 and 6

47. ganeshie8

$\frac{ (x-6)(x+3) }{ (x-7)(x+2)}$ plugging x=0 gives $\frac{ (0-6)(0+3) }{ (0-7)(0+2) }$ looks it is positive, yes ?

48. anonymous

YES!!

49. anonymous

so between -2 and 6 it's ok

50. anonymous

8 is negative then no

51. anonymous

and 7.5 is fine likewise

52. anonymous

so what we get is that -3>x, -2<x<6 and x>7

53. anonymous

you're brilliant! thank you so so much!!!!!!

54. anonymous

7.5 isn't good right

55. ganeshie8

|dw:1440159894339:dw|

56. ganeshie8

double check with wolfram http://www.wolframalpha.com/input/?i=solve+%28x%5E2-3x-18%29%2F%28x%5E2-5x-14%29%3E%3D0

57. anonymous

thanks a lot!!!!!

58. ganeshie8

np, the basic procedure for solving rational inequalities is : 1) factor both numerator and denomiantor 2) find the x values where the numerator or denominator equal 0 3) plot them on number line 4) pick a number in each interval and test the inequality

59. anonymous

@ganeshie8 is there any easier way to solve it?

60. ganeshie8

hmm i can't think of any other easy way to solve it.. post it again and see what others have to say..