## anonymous 5 years ago subtract: y/y-2 - 8+y/2-y

1. anonymous

This is tricky... you need to know this fact. 2 - y = -(y - 2) you can always flip numbers around a - sign and multiply by a - so 5 - x = -(x - 5)

2. anonymous

In this case you want the 2 - y to be y - 2 because you need a common denominator. so you turn the bottom in to y - 2 and then you put a - sign out in front... In this case that negative sign out front would turn your problem into a + sign y/y-2 + 8 + y/y - 2 Now you have common denominators y + 8 + y -------- y - 2 2y + 8 ------ y - 2

3. anonymous

omg hi again!!!

4. anonymous

this was our next question

5. anonymous

OK... I just found you... do you get this?

6. anonymous

i dont understand how you get the common denom....

7. anonymous

Well... y - 2 and 2 - y are opposites of each other.... you should be able to see that if you flip the one on the right around the minus sign it becomes the y - 2 ex. 2 - y flips to y - 2 OK?

8. anonymous

then you have to change the subtraction to addition??

9. anonymous

Yes... because it is the opposite you have to put a - sign out in front, and actually you change the sign of the problem... so in this case the subtraction becomes addition. This is a hard concept.

10. anonymous

hmmm then what

11. anonymous

Then you have a common denominator... so if you look above to my steps you will see that you put everything on the top over y - 2 because you now have a common denominator

12. anonymous

7/T-2 - 6/T^2-2T - 3/T is the LCD T^2-2T?

13. anonymous

7 6 3 ---- - ----------- - ------ T - 2 T^2 - 2T T T - 2 factors into (T - 2) T^2 - 2T factors into T(T - 2) T factors into T Common denominator is T(T - 2) or T^2 - 2T easier if you write it T(T - 2)

14. anonymous

T(T - 2) * 7 T(T - 2) * 6 T(T - 2) * 3 ------------ - ---------- - ---------- (T - 2) T(T - 2) T

15. anonymous

The (T - 2)'s cancel in the first fraction The T and (T - 2) cancel in the second fraction The T cancels in the third fraction

16. anonymous

7t-6-3t-2 ??

17. anonymous

7T - 6 - 3(t - 2) 7T - 6 - 3T + 6 4T

18. anonymous

isnt it -6?

19. anonymous

left with 4t-12

20. anonymous

The - sign goes with the 3 so it is actually -3(T - 2) and -3 * -2 = +6

21. anonymous

ohhh got it

22. anonymous

meeee tooooooo!

23. anonymous

YEAH!!!!!

24. anonymous

5-x/x-1 / 2-x/x+1

25. anonymous

5 - x 2 - x ---- divided by ----- x - 1 x + 1 write the divide sign that has a --- with a dot above and below. Are you sure this is what you want.

26. anonymous

noooo wait hold on

27. anonymous

X 5- ---- X-1 ___________ X 2- ---- X+1

28. anonymous

yes!

29. anonymous

OK... First we will simplify the top. 5 x - - ---- 1 x- 1 what is the common denominator?

30. anonymous

x-1?

31. anonymous

(x - 1)*5 x ------- - ----- x - 1 x - 1

32. anonymous

5x - 5 x ----- - ----- x - 1 x - 1 4x - 5 ------ x - 1 ok?

33. anonymous

5X+1-X --------- X-1

34. anonymous

GOT IT

35. anonymous

36. anonymous

Now let's do the same to the bottom.

37. anonymous

X+2 ----- X+1

38. anonymous

2 x - - ---- 1 x + 1 (x + 1)*2 x -------- - ---- (x + 1)*1 x + 1 (x + 1) *2 x -------- - ----- x + 1 x + 1 2x + 2 - x --------- x + 1 x + 2 ---- x + 1

39. anonymous

OOPS... go back to the first one... you have 4x - 1 look at mine... it is 4x - 5.. you have to distribute.

40. anonymous

got it

41. anonymous

4x - 5 x + 2 ------ divided by ------ x - 1 x + 1 Now.... when ever you have a fraction divided by a fraction. you ALWAYS multiply by the reciprocal

42. anonymous

4X+5 ------ X+1 -------- X+2 --- X+1

43. anonymous

4x - 5 x + 1 ------ x ----- x - 1 x + 2

44. anonymous

top right and bottom left cancel out?

45. anonymous

4X+5 ------ X+2

46. anonymous

amazing... go back and look at the numerator.. it is 4x - 5

47. anonymous

4X-5 ------ X+2 ????? I HOPE

48. anonymous

I wish they did cancel... they usually do.. but not here a (x - 1) can ONLY cancel with an (x - 1) and a (x + 1) can ONLY cancel with (x + 1) Usually you CAN cancel, but not in this problem. You would multiply the numerators (FOIL METHOD) then multiply the denominators (FOIL METHOD) and you would have your answer

49. anonymous

so now what!?!?!!? omg im lost now

50. anonymous

(4x - 5)(x + 1) ------------- (x - 1)(x + 2) 4x^2 + 4x - 5x - 5 ---------------- x^2 + 2x - x - 2 4x^2 - x - 5 ----------- x^2 + x - 2

51. anonymous

Unless you did not type in the original problem correctly? otherwise this is the answer.

52. anonymous

i got that

53. anonymous

Good.

54. anonymous

i wanna cry this is hard

55. anonymous

solve for X: (4x-7)^2 = -27 :)

56. anonymous

They are just a lot of steps.

57. anonymous

(4x - 7)^2 = -27 Are you sure this is correct?

58. anonymous

Yes

59. anonymous

yessssssssss

60. anonymous

OK.. so you know what imaginary numbers are i's

61. anonymous

yes !

62. anonymous

OK.. what if I gave you this problem... do you know what to do. x^2 = 16

63. anonymous

yes square root both sides

64. anonymous

Good... so in this problem you have (something)^2 = -27 so you square root both sides

65. anonymous

x=4

66. anonymous

(4x - 7)^2 = -27 4x - 7 = sqrt(-27)

67. anonymous

sqrt(-27) is -3i sqrt(3) do you understand this?

68. anonymous

$3i \sqrt{3?}$

69. anonymous

yess!

70. anonymous

OOPS you are correct is is positive

71. anonymous

4x - 7 = 3i sqrt(3) 4x = 3i sqrt(3) + 7 x = 3i sqrt(3) + 7 ------------ 4

72. anonymous

$9+3x-2x ^{2} \over x ^{2}-16$

73. anonymous

wait im not done hold on!

74. anonymous

all that divided by $4x ^{3}-9x \over 2x ^{2}+5x-12$

75. anonymous

simplify and state restricitons

76. anonymous

-2x^2 + 3x + 9 2x^2 + 5x - 12 --------------- x ------------- x^2 - 16 4x^3 - 9x since it is a fraction divide by a fraction.. we are going to turn it into a multiply problem right away by using the reciprocal. OK?

77. anonymous

ok hold on lemme take all that in

78. anonymous

then factor?

79. anonymous

yes we have to factor all four... but it is difficult to factor when there is a negative in front of the x^2 so for the first fraction in the numerator we are going to factor out a - sign first. - (2x^2 - 3x - 9)

80. anonymous

-(2x + 3)(x - 3) (2x - 3)(x + 4) -------------- x ------------- (x + 4)(x - 4) x(4x^2 - 9) x(2x + 3)(2x - 3)

81. anonymous

-(2x+3)(x-3) (x+4) (2x-3) ---------- ------------ (x+4) (x-4) x(2x+3) (2x-3)

82. anonymous

now we can cancel out right?

83. anonymous

Yes... now cancel anything in ( )'s with like ( )'s Anything on the top with anything on the bottom that matches.

84. anonymous

x-3 ----- x(x-4)

85. anonymous

close you still have that - sign on top -(x - 3) ------- x(x - 4) they may want it like -x + 3 ------ x^2 - 4x it is all the same...

86. anonymous

Now you also said you had to tell restrictions.

87. anonymous

yesss

88. anonymous

OK... go back to the factored fractions. The rule is you can NEVER divide by 0 so whatever makes those ( )'s 0 would be a restriction.

89. anonymous

We are only concerned with the denominators.

90. anonymous

okkk

91. anonymous

(x + 4)(x - 4) x(2x + 3)(2x - 3)

92. anonymous

-4,4 -3/2, 3/2

93. anonymous

And one more you need 0 because of the single x Every where there is an x there is a restriction.

94. anonymous

blexting you are great!!! we have 3 more can we keep going?

95. anonymous

Sure

96. anonymous

way better then our professor!

97. anonymous

X^2-9 ---------------- X^3+X^2-9X-9 SIMPLIFY

98. anonymous

Factor

99. anonymous

(x + 3)(x - 3) ------------

100. anonymous

When you have 4 terms you should try this first. Take the first two terms and take out a common factor. x^3 + x^2 = x^2(x + 1) Take the last two terms and do the same thing. -9x - 9 = -9(x + 1) OK?

101. anonymous

102. anonymous

(X^2-9) (X+1)

103. anonymous

I MEAN (X-1)

104. anonymous

OK.. Now you have x^2(x + 1) - 9(x + 1) ... good amozing. because (x + 1) is a common factor you now have (x + 1)(x^2 - 9) BUT this is the difference of two squares. (x + 1)(x + 3)(x - 3)

105. anonymous

they dont cancel out

106. anonymous

?

107. anonymous

So you have the top which is (x + 3)(x - 3) ------------ (x + 1)(x + 3)(x - 3) then cancel and you are left with 1 ------- x + 1 with restrictions of x cannot be -1,-3 or 3

108. anonymous

solve for X: 3 17 7 ------- = ---- - ----- 4x+2 2 2x+1

109. anonymous

Common denominator 4x + 2 = 2(2x + 1) 2 = 2 2x + 1 = 2x + 1 common denominator 2(2x + 1)

110. anonymous

Put that on top of each fraction and then cancel with the denominators.

111. anonymous

2(2x + 1) * 3 2(2x + 1) * 17 2(2x + 1) * 7 ----------- = ------------- - ----------- 2(2x + 1) 2 2x + 1

112. anonymous

34X+3=3 ??

113. anonymous

X=1/34

114. anonymous

3 = 17(2x + 1) - 14 3 = 34x + 17 - 14 3 = 34x + 3 0 = 34x 0 = x

115. anonymous

amozing when you take 34x + 3 = 3 and you subtract 3 you get 34x = 0

116. anonymous

Restrictions x cannot be -1/2

117. anonymous

GOT IT, THANKS!! ONE MORE :)

118. anonymous

OK

119. anonymous

X^2+XY-2Y^2 X ----------- X ----------------- X^3+X^2Y X^2+3XY+2Y^2

120. anonymous

3X^3Y^2

121. anonymous

NOT 3Y JUST Y SORRY

122. anonymous

(x + 2y)(x - y) x ------------ times -------------- x^2(x + y) (x + 2y)(x + y)

123. anonymous

(x - y) ------------ x(x + y)^2

124. anonymous

GOT IT THANKS!!

125. anonymous

gixxergirl..... did you leave us?

126. anonymous

Are we done????

127. anonymous

lol sorry i had to pee!!! but thank you so mucchhhhh for everythinggg !!! are you a math teacher?

128. anonymous

yes I am in a high school

129. anonymous

YOU HAVE BEEN SO HELPFUL!! THANK YOU SO MUCH

130. anonymous

No problem.. if you see me on here again and want help.. just holler. Have a wonderful Easter... He is risen!!! Good night.