## anonymous one year ago What is the simplified form of the quantity of x plus 7, all over the quantity of x plus 3 + the quantity of x minus 4, all over 3?

1. anonymous

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2. anonymous

@ganeshie8 @geerky42 @Michele_Laino

3. Michele_Laino

hint: the least common multiple between x+3 and 3 is: $3\left( {x + 3} \right)$

4. Michele_Laino

am I right?

5. anonymous

would it be x2++3x-28/3(x+3)

6. anonymous

Yes you are:)

7. Michele_Laino

so we can write this: $\Large \begin{gathered} \frac{{x + 7}}{{x + 3}} + \frac{{x - 4}}{3} = \hfill \\ \hfill \\ = \frac{{3\left( {x + 7} \right) + \left( {x + 3} \right)\left( {x - 4} \right)}}{{3\left( {x + 3} \right)}} = ... \hfill \\ \end{gathered}$ please continue

8. anonymous

(x+7)(x+3)(x-4)/3(X+3)

9. Michele_Laino

not exactly, since you have to compute the multiplications first

10. anonymous

hOW do I do that?

11. Michele_Laino

hint:

12. Michele_Laino

$3\left( {x + 7} \right) = 3x + 3 \times 7 = 3x + 21$

13. anonymous

3(x+7)

14. anonymous

I'm sorry :(

15. Michele_Laino

$\Large \left( {x + 3} \right)\left( {x - 4} \right) = x \cdot x - 4x + 3x - 4 \cdot 3 = ...$ here, I have applied the foil procedure

16. Michele_Laino

please simplify, what do you get?

17. anonymous

x^2-1x-12

18. Michele_Laino

ok!

19. Michele_Laino

so the numerator is: $\Large 3x + 21 + {x^2} - x - 12 = ...$

20. anonymous

2x+x^2+9

21. Michele_Laino

perfect! so your expression becomes: $\Large \frac{{x + 7}}{{x + 3}} + \frac{{x - 4}}{3} = \frac{{{x^2} + 2x + 9}}{{3\left( {x + 3} \right)}}$

22. anonymous

ohhh! Thank-you! I need one more please?

23. Michele_Laino

ok!

24. anonymous

What is the simplified form of the quantity of x plus 9, all over the quantity of 2x plus 3 + the quantity of x plus 4, all over the quantity of x plus 2?

25. Michele_Laino

26. anonymous

ok hold on

27. Michele_Laino

here the least common multiple is: $\left( {2x + 3} \right)\left( {x + 2} \right)$

28. Michele_Laino

is it right?

29. anonymous

Yes

30. anonymous

Now what?

31. Michele_Laino

ok! So we can write: $\large \frac{{x + 9}}{{2x + 3}} + \frac{{x + 4}}{{x + 2}} = \frac{{\left( {x + 9} \right)\left( {x + 2} \right) + \left( {x + 4} \right)\left( {2x + 3} \right)}}{{\left( {2x + 3} \right)\left( {x + 2} \right)}}$

32. Michele_Laino

now you have to apply the foil method in order to evaluate this: $\Large \left( {x + 9} \right)\left( {x + 2} \right) = ...?$

33. Michele_Laino

34. anonymous

x2+11x+18

35. Michele_Laino

ok! Now do the same with this expression: $\Large {\left( {x + 4} \right)\left( {2x + 3} \right)}$

36. anonymous

2x2+11x+12

37. Michele_Laino

ok! so the numerator is: $\Large {x^2} + 11x + 18 + 2{x^2} + 11x + 12 = ...$

38. anonymous

2x3+22x+30

39. Michele_Laino

are you sure?

40. anonymous

yes. wait no

41. anonymous

2x4+22x+30

42. Michele_Laino

I got: 3 x^2+...

43. Michele_Laino

$\Large {3{x^2} + 22x + 30}$

44. Michele_Laino

is it right?

45. anonymous

yes bcuz 1x2+2x2=3x2. I forgot about the imaginary 1

46. Michele_Laino

ok! So your original expression, becomes: $\Large \frac{{x + 9}}{{2x + 3}} + \frac{{x + 4}}{{x + 2}} = \frac{{3{x^2} + 22x + 30}}{{\left( {2x + 3} \right)\left( {x + 2} \right)}}$

47. anonymous

That's not an answer choice, so I guess we will have to foil the bottom also

48. Michele_Laino

ok! then what is: $\Large \left( {2x + 3} \right)\left( {x + 2} \right) = ...?$

49. anonymous

2x2+7x+6

50. Michele_Laino

so we get: $\Large \frac{{x + 9}}{{2x + 3}} + \frac{{x + 4}}{{x + 2}} = \frac{{3{x^2} + 22x + 30}}{{2{x^2} + 7x + 6}}$

51. Michele_Laino

yes! that's right!

52. anonymous

Yay! Ok so I want you to keep helping me, and give u medals, so i AM going to close the question and ask another ok?

53. Michele_Laino

I'm sorry, I have to go to dinner :(

54. anonymous

:( Ok well thanks anyways!

55. Michele_Laino

thanks! :)