## Tati_Lee 3 years ago simplify

1. Tati_Lee

$\frac{ 4x }{ 9 }+\frac{ x-10 }{ 9 }$

2. TheMind

so easy tati

3. TheMind

LCM=9

4. hartnn

common denominator so $$\huge \frac{4x+x-10}{9}$$

5. hartnn

whats 4x+x ?

6. Tati_Lee

thank i got it

7. Tati_Lee

$\frac{ 5x-10 }{ 9 }$ ?

8. Tati_Lee

@hartnn

9. hartnn

yup, thats correct :)

10. Tati_Lee

thank you can you help me with like 5 more ?

11. hartnn

only 5 ?

12. Tati_Lee

yes

13. hartnn

whats next ?

14. Tati_Lee

$\frac{ t^{2}+6 }{ t-1 }-\frac{ 7 }{ t-1 }$

15. hartnn

again common denominator, $$\frac{t^2+6-7}{t-1}$$

16. Tati_Lee

sorry the 6 has a t next to it

17. hartnn

whats 6-7 ?

18. hartnn

so can u factor t^2+6t-7 ?

19. Tati_Lee

umm yes ?

20. hartnn

then tell me the two factors....

21. Tati_Lee

ik you can factors that .. wouldnt one of the numbers be negative

22. hartnn

tell me 2 numbers whose sum is 6 and product is -7 yes,one of them is negative.

23. Tati_Lee

(t-6)(t+1) ??

24. hartnn

nice, its (t+7)(t-1) then cancel out t-1 from numerator and denominator what do u get finally ?

25. Tati_Lee

(t+7)

26. hartnn

thats it. :)

27. Tati_Lee

okay the next one $\frac{ 3 }{ x }+\frac{ 13 }{ x-11 }$

28. Tati_Lee

wouldnt the top be 16

29. hartnn

nopes,its not the same denominator now.

30. hartnn

u need to cross multiply..... can u ?

31. Tati_Lee

3x-33+13x

32. hartnn

yup,thats the correct numerator.... which will be 16x-33 and what will be denominator?

33. Tati_Lee

uhhh i dont know i thought the denominator would cancel out cross we crossed multiplied

34. hartnn

nopes it would be $$\huge \frac{16x-33}{x(x-11)}$$

35. Tati_Lee

ohh okay ... $\frac{ 5 }{ 4x ^{2}y }-\frac{ y }{ 14xy }$

36. Tati_Lee

??

37. hartnn

sorry, i kinda lost connection :( tell me the LCM of 4x^y and 14xy ?

38. Tati_Lee

oh okay it would be 2xy

39. hartnn

right, so can u solve that further ?

40. Tati_Lee

what do you mean?

41. hartnn

ok, i'll write next step, see it that makes sense $$\huge \frac{5(7)}{28x^2y}-\frac{y(2x)}{28x^2y}$$

42. Tati_Lee

ohh okay .. $\frac{ 35 }{28x ^{2}y }-\frac{ 2xy }{ 28x ^{2} y}$

43. Tati_Lee

then combine the denominator

44. hartnn

but did u get how i got that ? yes,then combine denom.

45. Tati_Lee

yea i saw you got that,

46. hartnn

so finally u get (35- 2xy)/(28x^2y) ok?

47. Tati_Lee

$\frac{ x ^{2}+2x }{12x+54 }-\frac{ 3x }{ 8x+36 }$

48. Tati_Lee

would i combine the like terms on the bottom & top

49. hartnn

nopes, first can u write 12x+54 as 6(2x+9) ??

50. Tati_Lee

you can cause that would equal the original equation

51. hartnn

so how would u write 8x+36 ?

52. Tati_Lee

8 doesn't go into 36 tho

53. Tati_Lee

36 doesnt go into 8 i mean

54. hartnn

what about 4 ? 36 and 8 both go into 4.

55. Tati_Lee

4(2x+9)

56. hartnn

right so u have $$\huge\frac{ x ^{2}+2x }{12x+54 }-\frac{ 3x }{ 8x+36 }=\frac{ x ^{2}+2x }{6(2x+9) }-\frac{ 3x }{ 4(2x+9) }$$ can u figure out next step ?

57. Tati_Lee

you would factor the top

58. hartnn

before that... $$\huge\frac{ x ^{2}+2x }{6(2x+9) }-\frac{ 3x }{ 4(2x+9) }=\frac{2( x ^{2}+2x) }{12(2x+9) }-\frac{ 4(3x) }{ 12(2x+9) }$$ u see how i tried to make the denominator same ?

59. hartnn

sorry it would be 3 in the numerator of 2nd fraction 3(3x)

60. Tati_Lee

i see it i see it it makes sense so then you would take away the denominator?

61. hartnn

take away ? since the denominator is common u combine the numerators. (2x^2+4x-9x)$$12(2x-9)) 62. Tati_Lee yea thats what i meant 63. Tati_Lee would the answer be 2x^2-5x/(12(2x-9) 64. hartnn yup, thats correct. (2x^2-5x)/(12(2x-9)) 65. Tati_Lee awesome .. there is one more 66. hartnn ok, ask. 67. Tati_Lee $\frac{ 2 }{ x ^{2}8x+15 } +\frac{ 1 }{ x ^{2} +11x+30}$ 68. Tati_Lee x^2 + 8 ** 69. hartnn can u factor both the quadratic polynomials in denom. ? 70. Tati_Lee i dont think so, im not sure 71. hartnn x^2+8x+15 = (x+5)(x+3) and x^2+11x+30=(x+5)(x+6) ok? 72. Tati_Lee ohhhhhh okay 73. Tati_Lee $\frac{ 3 }{ (x+3)(x+6) } or \frac{ 2 }{ (x+3) }+\frac{ 1 }{ (x+6)}$ 74. hartnn \(\large\frac{ 2 }{(x+5)(x+3)} +\frac{ 1 }{(x+5)(x+6)}=\frac{ 2(x+6) }{(x+6)(x+5)(x+3)} +\frac{ (x+3) }{(x+3)(x+5)(x+6)}$$ the idea is to make the denominator same, so that u can combine numerator....

75. Tati_Lee

oh okay

76. hartnn

so after combining numerators , u get 2x+12+x+3 = ?

77. Tati_Lee

3x+15

78. hartnn

can u take out something common from that?

79. Tati_Lee

5

80. hartnn

i would say 3 3(x+5)

81. Tati_Lee

82. hartnn

the numerator's (x+5) cancels with denominator's (x+5) to give u $$\huge \frac{3}{(x+3)(x+6)}$$

83. Tati_Lee

thank you soo much, you're amazing!

84. hartnn

welcome :) u too are awesome ;)

85. Tati_Lee

thanks ^_^