anonymous one year ago Find the sum and simplify and show all work and steps please..will give medals!! 2x/( x^2-x-12) + 3/ (x^2+4x+3)

1. Mertsj

Factor both denominators for the first step

2. Mertsj

What are the factors of x^2-x-12 ?

3. anonymous

I have no idea. Im very confused with this question

4. Mertsj

|dw:1442887631832:dw|

5. Mertsj

Think of two numbers whose product is -12

6. anonymous

6 & -2?? 12 & -1 ??

7. Mertsj

When you add the two numbers, you have to get -1 so think of some more possibilities.

8. anonymous

4 & -3

9. Mertsj

4+(-3)=1 The sum must be -1

10. anonymous

-4 & 3

11. Mertsj

Good.

12. Mertsj

|dw:1442887952257:dw|

13. Mertsj

So now you have factored the first denominator. Try the second one.

14. anonymous

X^2+4x+3 = (x+3)(x+1)

15. Mertsj

So now we have this problem: $\frac{2x}{(x-4)(x+3)}+\frac{3}{(x+1)(x+3)}$

16. Mertsj

Now we have to get the common denominator so we can add the two fractions.

17. Mertsj

For the first denominator we need the factors (x-4)(x+3) For the second denominator we need the factors (x+1)(x+3)

18. Mertsj

So the factors we need are (x-4) and (x+3) and (x+1) and that is the common denominator. Are you with me so far?

19. anonymous

Yes

20. Mertsj

So the first fraction will have to be multiplied by (x+1)/(x+1) to get the denominator right.

21. Mertsj

The second fraction will have to be multiplied by (x-4)(x-4) to get the denominator right. Do you agree?

22. anonymous

Yes

23. Mertsj

$\frac{2x}{(x-4)(x+3)}\times \frac{(x+1)}{(x+1)} + \frac{3}{(x+1)(x+3)}\times \frac{(x-4)}{(x-4)}$

24. Mertsj

So now if we do the multiplication we have:

25. Mertsj

$\frac{2x^2+2x+3x-12}{(x+1)(x+3)(x-4)}$

26. Mertsj

Still ok with this?

27. anonymous

Yes

28. Mertsj

So let's add the like terms and finish up.

29. Mertsj

$\frac{2x^2+5x-12}{(x+1)(x+3)(x-4)}$

30. anonymous

Is that the final answer?? It doesnt simplify down anymore??

31. Mertsj

You could try to factor the numerator but I don't think it will factor. Are there factors of -24 whose sum is 5?

32. anonymous

I dont think so. The correct answer would be 2x^2+5x-12 / (x+1)(x+3)(x-4) ?

33. Mertsj

Oh it will factor. The factors are (2x-3)(x+4)

34. Mertsj

So now we have: $\frac{(2x-3)(x+4)}{(x+1)(x+3)(x-4)}$

35. Mertsj

But there are no common factors to cancel so our answer is correct.

36. anonymous

So the (2x-3)(x+4) and so on the correct answerr??

37. Mertsj

The answer is: $\frac{2x^2+5x-12}{(x+1)(x+3)(x-4)} or \frac{(2x-3)(x+4)}{(x+1)(x+3)(x-4)}$

38. Mertsj

because they are two forms of the same answer

39. Mertsj

So you can take your pick.

40. anonymous

Oh okay i understand (: thank you so much!

41. Mertsj

yw