anonymous one year ago Help solve please medal! Simplify 3x+10/ x+1 + x+3/x+4 -6x+27/(x+1)(x+4)

1. anonymous

2. anonymous

@Yungwisdom2000 @Compassionate

3. jtvatsim

I'm going to rewrite this to make sure we are looking at the same thing. :)

4. anonymous

ok thanks :)

5. jtvatsim

$\frac{3x+10}{ x+1} + \frac{ x+3}{x+4} - \frac{6x+27}{(x+1)(x+4)}$ Is that the right thing?

6. anonymous

correct

7. jtvatsim

It's a bit scary looking. :) Any thoughts on what you might do first?

8. anonymous

we need a common denominator right :)

9. jtvatsim

That would be REALLY nice. Yes, let's try that.

10. jtvatsim

What might be the common denominator we are trying to make?

11. anonymous

(x+1) (x+4) right

12. jtvatsim

Seems like a good choice. That appears to be the most complicated thing in our expression. So far, so good.

13. jtvatsim

So, let's look at the first fraction. What needs to be done here?

14. anonymous

3x+10 (x+4) / x+1 (x+4) + (x+3) (x+1) / (x+4)(x+4) right

15. jtvatsim

Yes, on the second fraction you mean (x + 1) on the bottom, but I get it. :)

16. jtvatsim

Great! So here's what we have so far.

17. jtvatsim

$\frac{(3x+10) (x + 4)}{(x+1) (x + 4)}+\frac{(x+3)(x+1)}{(x+1)(x+4)}−\frac{6x+27}{(x+1)(x+4)}$

18. jtvatsim

Wow, that's a lot of stuff. Now what?

19. anonymous

cancel out

20. jtvatsim

Well, if we "cancel out" that might put us right back where we started right? Unless you mean distribute...

21. anonymous

i'm sorry i meant distribute lol

22. jtvatsim

No worries. :) Let's try to do that. What do you get. (Might take a minute) :)

23. anonymous

im kinda lost can you draw it out

24. anonymous

from where we left off

25. jtvatsim

Sure! I think we were here right? $\frac{(3x+10)(x+4)}{(x+1)(x+4)}+\frac{(x+3)(x+1)}{(x+1)(x+4)}−\frac{6x+27}{(x+1)(x+4)}$

26. anonymous

yes ok, so we distribute

27. jtvatsim

Yes, and what do you get after that?

28. anonymous

i got 4/ (x+1) (x+4)

29. jtvatsim

4 for which fraction?

30. jtvatsim

31. anonymous

yes the final

32. anonymous

i think i did something wrong

33. jtvatsim

Oh, ok, let me double check that. :)

34. anonymous

35. jtvatsim

So, for the first fraction: $\frac{(3x+10)(x+4)}{(x+1)(x+4)}=\frac{3x^2 + 12x + 10 x + 40}{(x+1)(x+4)}$

36. jtvatsim

For the second fraction: $\frac{(x+3)(x+1)}{(x+1)(x+4)} = \frac{x^2 + 3x + x + 3}{(x+1)(x+4)}$

37. jtvatsim

For the third fraction (watch out for the tricky - sign!): $-\frac{6x+27}{(x+1)(x+4)}=\frac{-6x-27}{(x+1)(x+4)}$

38. anonymous

ok i got 1/ (x+4)(x+1) for final

39. jtvatsim

Checking again... :)

40. jtvatsim

I get: (3x^2 + x^2 + 22x + 4x - 6x + 40 + 3 - 27)/(x+1)(x+4) so (4x^2 + 20x + 16)/(x+1)(x+4) so (2x + 2)(2x + 8)/(x+1)(x+4) then 2(x+1)*2(x+4)/(x+1)(x+4) Oh wow! 4 is the final answer. I think. :)

41. anonymous

ok i see, now you factor

42. anonymous

hey do you mind checking this one for me

43. anonymous

x/3 div 2/x+5

44. anonymous

i got X(x+5) /6

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