Question

(3/x-3) + (x/x+3) = ?
Show the work? I dont know how to make the denominators the same.

Answer 1

You need to find the LCM (aka LCD) of each of the denominators

Answer 2

(x-3)(x+3)?

Answer 3

Yep. So now you want to multiply each fraction by the one that it's missing. The first fraction is missing the x+3. So multiply that fraction by (x+3)/(x+3)

Answer 4

That will make the denominator match your LCD, and the numerator will be 3(x+3)

Answer 5

Then for the second fraction, it's missing x-3, so multiply it by (x-3)/(x-3)

Answer 6

That will again make the denominator match your LCD, and the numerator will be x(x-3)

Answer 7

Now you can add the two fractions and simplify.

Answer 8

What do you have after you did all that, just to make sure you didn't make a mistake

Answer 9

Well, I got 3x.... & i dont think that sounds right...

Answer 10

What did you have for the fractions when you changed denominators?

Answer 11

\[\frac{3(x+3)}{(x+3)(x-3)} + \frac{x(x-3)}{(x+3)(x-3)}\]
Right?

Answer 12

You did that alot faster than I could... but yeah, thats what I got!

Answer 13

Ok so now when you add them:
\[=\frac{3(x+3) + x(x-3)}{(x+3)(x-3)}\]

Answer 14

Then dont the (x+3)'s on the left side of the addition sign cancel out?

Answer 15

They do, but you don't want to do that cause then your denominators will be different again

Answer 16

And you won't be able to add them

Answer 17

Shoot, okay... & where do you go from there.. just distribute on the top?

Answer 18

Yep, distribute then combine like terms

Answer 19

Let me know what you get in the numerator and I'll check it

Answer 20

Isn't it 5x+6?

Answer 21

wait.

Answer 22

2x+9

Answer 23

Sike; x^2 + 9.. took me long enough to make a thousand mistakes.

Answer 24

\[3(x+3) + x(x-3)\]\[=3x + 9 + x^2 - 3x\]\[= x^2 + 9\]

Answer 25

Right, haha, sorry.(:

Answer 26

Right. So your answer is:
\[\frac{x^2+9}{(x+3)(x-3)}\]

Answer 27

What do you do with the bottom? Foil it?

Answer 28

Sure if you want to

Answer 29

Probably that's how they want it, though I prefer factored personally

Answer 30

Right? Me too. Well thank you very much! You were lots of help!

Answer 31

Certainly. Just remember when you need to add/subtract fractions with dissimilar denominators you must use this process:

1) factor the denominators
2) find the LCD for all of the fractions
3) multiply each fraction (top & bottom) by the factors
it's missing
4) add/subtract the fractions together over the
common denominator
5) distribute and simplify the numerator
6) cancel any common factors in the top/bottom to
reduce

Answer 32

Alright; will do! Thanks(: