2x 4 12 (2-x)
--- / ---- + ---- X ---
(x^2-4) (x^2-4x+4) (x^2-4) 3
You aren't following instructions very well. LOOK AT YOUR POST and you will see that you can't space it this way. Look back at your original post for my suggestion on how to post a problem of this kind. We can't help if we can't make heads or tails of the question.
ok ill do it like this ...
2x over x squared - 4 divided by 4 over x squared - 4x + 4 plus 12 over x squared - 4 multiplied by 2-x over 3
Is this it? And what do you want to do with it?
{[2x/(x^2-4)]/(4/x^2-4x+4)} + [12/(x^2-4)]*[(2-x)/3]
yess that's it .. it has to be expressed in simplest form - im sorry for the misunderstanding thank you very much for any help that you can give
Since you agreed with DrBob's way of writing your problem, let's take it in parts
The first term reduces to
[2x/((x+2)(x-2))]*[(x-2)(x-2)/4
= x(x-2)/[2(x+2)]
the second term [12/(x^2-4)]*[(2-x)/3]
= 12/[(x-2)(x+2)]*(2-x)/3
= -4/(x+2)
using a common denominator of 2(x+2)
we get :
= (x^2 - 2x - 4)/[2(x+2)]
= (x-4)(x+2)/[2(x+2)]
= (x-4)/2 , x cannot be -2
To simplify the given expression:
1. Start by factoring the denominators of each fraction in the numerator.
- For the first fraction, factor the denominator `(x^2-4)`. It can be factored as `(x+2)(x-2)`.
- For the second fraction, factor the denominator `(x^2-4x+4)`. It is a perfect square trinomial and can be factored as `(x-2)^2`.
- The third fraction has a denominator of `(x^2-4)`, which is the same as the first fraction.
2. Now rewrite the expression with the factored denominators:
`2x/(x+2)(x-2) + 4/(x-2)^2 + 12(x-2)/(x+2)(x-2) * 3`
3. Simplify the expression further:
- Combine the fractions over a common denominator, which is `(x+2)(x-2)`.
- Multiply the numerators of each fraction by the other denominators to eliminate the denominators:
`(2x)(x-2) + 4(x+2)(x+2) + 12(x-2)(3)`
- Distribute and simplify the resulting expression:
`2x^2 - 4x + 4x^2 + 16 + 36x - 72`
`6x^2 + 32x - 56`
So, the simplified form of the expression is `6x^2 + 32x - 56`.