how do you simplify.........?

Question

3/x-2+6/x+2....this is algebra2...steps if possible...thank you in advance.....

Answer 1

3/(x-2) + 6/(x+2)
= 3*(x-2)/[(x-2)(x+2)] + 6*(x+2)/[(x-2)(x+2)]
= (3x-6)/[(x-2)(x+2)] + (6x+12)/[(x-2)(x+2)]
=(3x-6+6x+12)/[(x-2)(x+2)]
=(9x+6)/[(x-2)(x+2)]
=(9x+6)/(x^2-4)

Answer 2

First, you would probably want to get a common denominator.

This will be (x-2)(x+2). To do this, multiply each part by what it is missing from the other part:

(3(x+2) + 6(x-2))/((x-2)(x+2))

Then, multiply each part to get:

3x+6 + 6x-12 in the numerator. We will leave the denominator in factored form for now, in case anything would cancel from the numerator.

So now you add all the like terms to get:

9x -6 in the numerator, and (x-2)(x+2) in the denominator.

You can factor 9x-6, but all you end up with is 3(3x-2), and that won't get anything from the denominator to cancel, so your final answer will be:

(9x-6)/((x-2)(x+2) or you can multiply out the denominator to get x^2-4. Either way is acceptable.

Zach D's answer above is incorrect because + and - 2 are not factors of (multiplied by) anything in either the numerator or denominator. They would be factors and could cancel out if the problem looked like: (2(x-2))/(2(x+2)) In this case, the two's are multiples of the parenthetical expressions, and thus can be cancelled out.

ComputerHelpNeeded's answer is almost right, but a simple mistake was made right at the beginning in the copying down of the problem---this person miswrote 1(x-2) instead of 3(x-2) and the whole problem carried this simple mistake all the way through to get the wrong answer.

Answer 3

I'm assuming we have 3/(x-2) + 6/(x+2)

In order to combine these two fractions, we need to find a common denominator (it all gets back to fractions... Fractions are really not the horrible thing we think they are)

Multiply the first by (x+2)/(x+2) and the second by (x-2)/(x-2):
(3x+6)/(x^2-4) + (6x-12)/(x^2-4)
=
(3x+6+6x-12)/(x^2-4) =
(9x-6)/(x^2-4)
Don't think I can reduce that any more.

Answer 4

Do the following steps

1 Get same denominator
So you have--> 1(x+2)/((x+2)(x-2)) + 6(x-2)/((x+2)(x-2))

2 Realize that (x+2)(x-2) = x^2 - 2^2 = x^2 - 4
This is because of the property: (a+b)(a-b) = a^2 - b^2

3 Take common denominator
So you have--> ((x+2)+6(x-2))/(x^2-4)

4 Simplify numerator
So you have--> (x+2+6x-12)/(x^2-4)
And --> (7x-10)/(x^2-4)

THAT'S IT!!!

Answer 5

3/x - 2 + 6/x + 2 = -3/x

-2 and +2 cancel each other out, so essentially you have

3/x - 6/x = which is, -3/x

Answer 6

(3/(x-2)) + (6/(x+2))

get the lcd which is x^2-4

so,
3x+6/(x^2-4) + 6x-12/(x^2-4)

combine like terms,
9x-6/(x^2-4) <--answer.. :)

Answer 7

= [ 3.(x + 2) + 6.(x - 2) ] / [(x + 2).(x - 2)]
= [ 9x - 6 ] / [(x + 2).(x - 2)]
= 3.(3x - 2) / [(x + 2).(x - 2)]