anonymous
  • anonymous
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)
Mathematics
katieb
  • katieb
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Mertsj
  • Mertsj
Factor both denominators for the first step
Mertsj
  • Mertsj
What are the factors of x^2-x-12 ?
anonymous
  • anonymous
I have no idea. Im very confused with this question

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Mertsj
  • Mertsj
|dw:1442887631832:dw|
Mertsj
  • Mertsj
Think of two numbers whose product is -12
anonymous
  • anonymous
6 & -2?? 12 & -1 ??
Mertsj
  • Mertsj
When you add the two numbers, you have to get -1 so think of some more possibilities.
anonymous
  • anonymous
4 & -3
Mertsj
  • Mertsj
4+(-3)=1 The sum must be -1
anonymous
  • anonymous
-4 & 3
Mertsj
  • Mertsj
Good.
Mertsj
  • Mertsj
|dw:1442887952257:dw|
Mertsj
  • Mertsj
So now you have factored the first denominator. Try the second one.
anonymous
  • anonymous
X^2+4x+3 = (x+3)(x+1)
Mertsj
  • Mertsj
So now we have this problem: \[\frac{2x}{(x-4)(x+3)}+\frac{3}{(x+1)(x+3)}\]
Mertsj
  • Mertsj
Now we have to get the common denominator so we can add the two fractions.
Mertsj
  • 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)
Mertsj
  • 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?
anonymous
  • anonymous
Yes
Mertsj
  • Mertsj
So the first fraction will have to be multiplied by (x+1)/(x+1) to get the denominator right.
Mertsj
  • Mertsj
The second fraction will have to be multiplied by (x-4)(x-4) to get the denominator right. Do you agree?
anonymous
  • anonymous
Yes
Mertsj
  • Mertsj
\[\frac{2x}{(x-4)(x+3)}\times \frac{(x+1)}{(x+1)} + \frac{3}{(x+1)(x+3)}\times \frac{(x-4)}{(x-4)}\]
Mertsj
  • Mertsj
So now if we do the multiplication we have:
Mertsj
  • Mertsj
\[\frac{2x^2+2x+3x-12}{(x+1)(x+3)(x-4)}\]
Mertsj
  • Mertsj
Still ok with this?
anonymous
  • anonymous
Yes
Mertsj
  • Mertsj
So let's add the like terms and finish up.
Mertsj
  • Mertsj
\[\frac{2x^2+5x-12}{(x+1)(x+3)(x-4)}\]
anonymous
  • anonymous
Is that the final answer?? It doesnt simplify down anymore??
Mertsj
  • 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?
anonymous
  • anonymous
I dont think so. The correct answer would be 2x^2+5x-12 / (x+1)(x+3)(x-4) ?
Mertsj
  • Mertsj
Oh it will factor. The factors are (2x-3)(x+4)
Mertsj
  • Mertsj
So now we have: \[\frac{(2x-3)(x+4)}{(x+1)(x+3)(x-4)}\]
Mertsj
  • Mertsj
But there are no common factors to cancel so our answer is correct.
anonymous
  • anonymous
So the (2x-3)(x+4) and so on the correct answerr??
Mertsj
  • Mertsj
The answer is: \[\frac{2x^2+5x-12}{(x+1)(x+3)(x-4)} or \frac{(2x-3)(x+4)}{(x+1)(x+3)(x-4)}\]
Mertsj
  • Mertsj
because they are two forms of the same answer
Mertsj
  • Mertsj
So you can take your pick.
anonymous
  • anonymous
Oh okay i understand (: thank you so much!
Mertsj
  • Mertsj
yw

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