## anonymous one year ago Divide and simplify completely.

1. anonymous

|dw:1433180002271:dw|

2. anonymous

ok!

3. anonymous

okay! thank you so much!!:D

4. anonymous

@mathstudent55

5. anonymous

@paki

6. Luigi0210

Start by factoring then changing that division to multiplication.

7. anonymous

can we do it on the drawing tool?

8. anonymous

@Luigi0210

9. Luigi0210

Sure, like I said, start factoring, what do you get?

10. anonymous

do i start with writing the whole problem? orjust the first two fractions?

11. Luigi0210

Writing the whole problem would be better, it'll help see where things might cancel.

12. anonymous

13. anonymous

|dw:1433181469815:dw|

14. anonymous

@Luigi0210

15. Luigi0210

Okay, so start by changing the division to multiplication, do you know how?

16. anonymous

@Luigi0210 i had to change laptobs, so there will be no more lagging!

17. Luigi0210

Alright, so do you know how to change the operations from division to multiplication?

18. anonymous

im not so sure! @Luigi0210

19. Luigi0210

Alright, so in order to switch it, you flip the fraction and then change the sign, like so: $$\large \frac{a}{b} \div \frac{c}{d}$$ becomes $$\large \frac{a}{b} \times \frac{d}{c}$$ make sense?

20. anonymous

yes

21. Luigi0210

Alright, try applying it to this part: $$\large \frac{6x+6}{x^2-1} \times \color{green}{\frac{x-1}{8x^2-24x} \div \frac{24}{x^2-9}}$$

22. anonymous

ok |dw:1433183061134:dw|

23. Luigi0210

Right, now let's start factoring, what these factor to: $$\large x^2-1=$$ $$\large 6x+6=$$ $$\large 8x^2-24x=$$ $$\large x^2-9=$$

24. anonymous

|dw:1433183782053:dw|

25. anonymous

@Luigi0210

26. Nnesha

apply difference of square method a^2 - b^2 = (a+b)(a-b)

27. Nnesha

so x^2 - 9 = ?

28. anonymous

@Nnesha

29. Nnesha

yes ?

30. anonymous

im not sure what that equals to?

31. Nnesha

difference of square take square root of first term and 2nd term write in two parentheses (sqr root of first term + square root of 2nd term ) ( sqr root of first term - square root of 2nd term) a^2 - b^2 = (a+b)(a-b)

32. anonymous

ok

33. Nnesha

so x^2 - 9 = ?

34. anonymous

|dw:1433185790534:dw|

35. anonymous

@Nnesha

36. Nnesha

|dw:1433185969475:dw| take square root of both terms

37. anonymous

|dw:1433186021089:dw|

38. Nnesha

what is square root of 9 ?

39. anonymous

|dw:1433186054040:dw|

40. Nnesha

yes that's right

41. Nnesha

$$\huge\rm \frac{6x+6}{x^2-1} \times \color{green}{\frac{x-1}{8x^2-24x} \div \frac{24}{x^2-9}}$$ alright first of change division to multiplication

42. Nnesha
43. anonymous

|dw:1433186323191:dw|

44. Nnesha

ys right

45. Nnesha

i have to go i'll be here after 15 mints

46. anonymous

|dw:1433186435230:dw|

47. anonymous

@Nnesha

48. anonymous

@Luigi0210

49. anonymous

|dw:1433186564993:dw|

50. Nnesha

|dw:1433186742147:dw| now factor 6x-6 x^2 -1 8x^2 -24x

51. anonymous

@Nnesha how do i do that?

52. anonymous

@Michele_Laino @Nnesha

53. Nnesha

same method for x^2-1 difference of square

54. anonymous

how do i do that? can you show me on the drawing tool????

55. Nnesha

it's same like last one square root of first number and square root of 2nd number

56. Nnesha

|dw:1433188107357:dw| just like this one

57. anonymous

with what numbers?

58. Nnesha

x^2 - 1 first term is x^2 2nd term is 1

59. anonymous

|dw:1433188199277:dw|

60. Nnesha

|dw:1433188239145:dw| take SQUARE ROOT of first and last term what is square root of x^2 ?

61. anonymous

|dw:1433188302499:dw|

62. Nnesha

square root of 1 is just one

63. anonymous

|dw:1433188379947:dw|

64. Nnesha

yes right (x +1 ) (x-1)

65. anonymous

ok

66. Nnesha

$$\huge\rm \frac{6x+6}{(x+1)(x-1)} \times \color{green}{\frac{x-1}{8x^2-24x} \times \frac{24}{(x-3)(x+3)}}$$ now factor 6x+6 what is commin in these both term ?

67. anonymous

they both have 6

68. Nnesha

yes right take it out

69. Nnesha

6x+6 6( ) what should go in the parentheses ?

70. anonymous

so you are left with x?

71. Nnesha

nope divide both term by 6 so 6/6 = ?

72. anonymous

2

73. Nnesha

6 divide by 6 = ?

74. anonymous

is 1

75. Nnesha

yes right so it's 6(x+1)

76. Nnesha

$$\huge\rm \frac{6(x+1)}{(x+1)(x-1)} \times \color{green}{\frac{x-1}{8x^2-24x} \times \frac{24}{(x-3)(x+3)}}$$ ahh last one factor 8x^2 -24x

77. anonymous

what whould it be for 8x^2?

78. Nnesha

x^2 ? lowest degree of x would be common term and yes 8 is right and what else ?

79. anonymous

ok

80. anonymous

81. Nnesha

yes so 8 is common what about variable ?

82. anonymous

the variable is x!

83. Nnesha

yes right so 8x is out what should goe in parentheses ??

84. anonymous

umm im not sure?

85. Nnesha

|dw:1433189936138:dw| divide both term by 8x

86. anonymous

so x and 3?

87. Nnesha

yep right

88. anonymous

yayy!!!

89. Nnesha

wait

90. Nnesha

it's $$\huge\rm \frac{6(x+1)}{(x+1)(x-1)} \times \color{green}{\frac{x-1}{8x(x-3)} \times \frac{(x-3)(x+3)}{ 24}}$$ start canceling stufffff

91. anonymous

|dw:1433190165667:dw|

92. Nnesha

$$\huge\rm \frac{6\cancel{(x+1)}}{\cancel{(x+1)}\cancel{(x-1)}} \times \color{green}{\frac{\cancel{x-1}}{8x\cancel{(x-3)}} \times \frac{\cancel{(x-3)}(x+3)}{ 24}}$$ $\frac{ 6(x+3) }{ 8x \times 24 }$ 6/24 ?

93. anonymous

ok

94. anonymous

|dw:1433190834800:dw|

95. Nnesha

nopw that's not a pllus sgn

96. Nnesha

|dw:1433190954018:dw|reduse the fraction

97. Nnesha

reduce *

98. anonymous

1/4

99. anonymous

for some reason it whould not post but, i got it!!

100. Nnesha

$$\huge\rm \frac{6\cancel{(x+1)}}{\cancel{(x+1)}\cancel{(x-1)}} \times \color{green}{\frac{\cancel{x-1}}{8x\cancel{(x-3)}} \times \frac{\cancel{(x-3)}(x+3)}{ 24}}$$ $\frac{ 1(x+3) }{ 8x \times 4 }$ now multiply

101. Nnesha

4 times 8x = ? done!

102. anonymous

32x ! @Nnesha

103. Nnesha

yep right x+3/32x

104. anonymous

so the answer is c? @Nnesha

105. Nnesha

where are the answer choices ?