## Bananas1234 one year ago Find the LCD of both fractions, then simplify the expression. Assume that no denominator equals zero. 5/3x^2y - 4/6xy^3

1. Bananas1234

@JoannaBlackwelder

2. Bananas1234

@Nnesha

3. JoannaBlackwelder

The LCD is finding the smallest denominator that makes them both the same.

4. JoannaBlackwelder

Do you have any ideas of how to start doing that?

5. Bananas1234

how do i find that?

6. Bananas1234

not sure, sorry

7. JoannaBlackwelder

Ok, the two denominators are|dw:1433440171339:dw|

8. JoannaBlackwelder

I mean... |dw:1433440214478:dw|

9. Bananas1234

ok

10. JoannaBlackwelder

If we multiply the left one by 2, we get a common coefficient|dw:1433440278787:dw|

11. JoannaBlackwelder

Do you see how that gives us a common coefficient of 6?

12. JoannaBlackwelder

|dw:1433440359049:dw|

13. Bananas1234

yes, because 2 times 3 is 6?

14. JoannaBlackwelder

Right.

15. JoannaBlackwelder

And we have 2 x's on the left, but only 1 on the right.

16. JoannaBlackwelder

So we need to multiply the right side by x to make the number of x's the same

17. JoannaBlackwelder

|dw:1433440468526:dw|

18. Bananas1234

i see

19. JoannaBlackwelder

:-) How do you think we can make the number of y's the same?

20. Bananas1234

times it by y?

21. JoannaBlackwelder

Close. That would give us:|dw:1433440631552:dw|

22. JoannaBlackwelder

So the numbers of y's still aren't quite the same.

23. Bananas1234

they arent?

24. Bananas1234

ok whats next

25. JoannaBlackwelder

It looks like we have 2 y's on the left, but 3 on the left.

26. Bananas1234

i see

27. Bananas1234

you mean 3 on the right?

28. JoannaBlackwelder

Yeah, sorry.

29. Bananas1234

ok

30. JoannaBlackwelder

So, we need one more y on the left.

31. Bananas1234

ok, so do we mulitply again?

32. JoannaBlackwelder

Yep

33. Bananas1234

|dw:1433440911998:dw|

34. JoannaBlackwelder

Yep, great! So, are the denominators the same now?

35. Bananas1234

yes

36. JoannaBlackwelder

Great! So, in the full problem, how do we make that both denominators?

37. Bananas1234

|dw:1433441111648:dw|

38. Bananas1234

Like that?

39. JoannaBlackwelder

But we can't just change the denominators. We have to also change the numerators to keep everything balanced.

40. Bananas1234

41. Bananas1234

ow do we do that?

42. Bananas1234

how*

43. JoannaBlackwelder

What do we need to multiply by the first denominator to get it to be our LCM?

44. JoannaBlackwelder

*LCD

45. Bananas1234

not sure, sorry.

46. JoannaBlackwelder

|dw:1433441688086:dw|

47. Bananas1234

what do i put in the (?)?

48. Bananas1234

@JoannaBlackwelder

49. JoannaBlackwelder

What did we multiply by to get the LCD of the left side?

50. Bananas1234

by y?

51. JoannaBlackwelder

Was that all?

52. Bananas1234

i think so....

53. JoannaBlackwelder

No, |dw:1433442752287:dw| so we need to multiply the left fraction on top and bottom by 2y^2

54. Bananas1234

oh

55. JoannaBlackwelder

|dw:1433442908806:dw|

56. JoannaBlackwelder

Can you simplify?

57. Bananas1234

how do i simplify??

58. JoannaBlackwelder

Multiply

59. Bananas1234

multiply the 5 by the 2y^2?

60. JoannaBlackwelder

Yep

61. Bananas1234

10y^2/6x^2y^3?

62. JoannaBlackwelder

Yep, great! How about the other fraction?

63. Bananas1234

|dw:1433443839427:dw| Like this??

64. Bananas1234

so 8y2/12xy^5?

65. Bananas1234

8y^2/12xy^5 @JoannaBlackwelder

66. Bananas1234

is that all i need to do? @JoannaBlackwelder

67. Bananas1234

please reply i have 20 mins to get this done :( @JoannaBlackwelder

68. JoannaBlackwelder

Sorry, I was doing some online tutoring. But no, we didn't multiply by 2y^2 on the right fraction to get the LCD.

69. Bananas1234

ok

70. JoannaBlackwelder

|dw:1433445935170:dw|

71. JoannaBlackwelder

We need to multiply the right fraction by x to make common denominators.

72. Bananas1234

i got that part

73. JoannaBlackwelder

|dw:1433446083616:dw|

74. Bananas1234

i see

75. JoannaBlackwelder

:-)

76. JoannaBlackwelder

|dw:1433446145225:dw|

77. JoannaBlackwelder

So, now we can subtract the numerators, and the denominators stay the same.

78. JoannaBlackwelder

So, what does that give us?

79. Bananas1234

6y^2x?

80. JoannaBlackwelder

No, I mean for the whole fraction.

81. Bananas1234

im having a hard time subtracting the bottom

82. JoannaBlackwelder

It stays the same. Doesn't subtract.

83. Bananas1234

ohh i see

84. JoannaBlackwelder

|dw:1433446648437:dw|

85. Bananas1234

so,6y^2x/6x^2y^3

86. JoannaBlackwelder

No, only like terms can add.

87. Bananas1234

ok

88. Bananas1234

so its 10y^2 - 4x/6x^2y^3 is that all??

89. JoannaBlackwelder

Well, we can simplify a bit by factoring out a 2

90. Bananas1234

what 2?

91. Bananas1234

i do have to get this turned in now, if i don't i will get a 0

92. Bananas1234

the 2 on 6 and 10??

93. JoannaBlackwelder

Yes, and the 4

94. JoannaBlackwelder

You can turn it in like that. You should get partial credit

95. Bananas1234

ok, but if i were to do it some other time what can i do?

96. JoannaBlackwelder

|dw:1433447702331:dw|

97. Bananas1234

ok, thank you for all of your help, sorry that took so long.

98. JoannaBlackwelder

And the twos cancel out. |dw:1433447840612:dw|

99. JoannaBlackwelder

You're welcome :-)