Question

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)

Answer 1

Factor both denominators for the first step

Answer 2

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

Answer 3

I have no idea. Im very confused with this question

Answer 4

Think of two numbers whose product is -12

Answer 5

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

Answer 6

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

Answer 7

4 & -3

Answer 8

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

Answer 9

-4 & 3

Answer 10

Good.

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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?

Answer 17

Yes

Answer 18

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

Answer 19

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

Answer 20

Yes

Answer 21

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

Answer 22

So now if we do the multiplication we have:

Answer 23

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

Answer 24

Still ok with this?

Answer 25

Yes

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

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

Answer 33

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

Answer 34

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

Answer 35

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

Answer 36

because they are two forms of the same answer

Answer 37

So you can take your pick.

Answer 38

Oh okay i understand (: thank you so much!

Answer 39

yw