Question

Hi, could someone give me a step by step explanation of how to solve this problem?
(3x)/(x+2) + (x)/(x-2) - (4)/(x²-4)

Answer 1

So far this is what I have done:

Answer 2

\[3x/(x+2) + x/(x-2) + -(4)/(x+2)(x-2)\]
Made the common denominator-
(x+2)(x-2)

\[(3x)(x-2) + (x)(x+2) +(-4)(x-2)\]
Multiply that out...
\[3x²-6x+x²+2x+(-4x)-8\]

Answer 3

Sorry, your question is unclear. What is the problem exactly?

Answer 4

3x x 4x
--- + --- - ---
x+2 x-2 x²-4

Answer 5

Those dashed lines are supposed to represent the lines in fractions. :/

Answer 6

x²-4=(x+2)(x-2)

You'll need to have the same denominator for all fractions to simplify the equation.
1=(x+2)/(x+2) eqn1
1=(x-2)(x-2) eqn2

3x/(x+2) =(3x/(x+2))*1
x/(x-2)=(x/(x-2))*1

4x/(x²-4) will remain the same since both (x+2) and (x-2) are factors of x²-4
Subsitute both 1s with eqn1 and eqn2 respectively to obtain the (x²-4) denominator.

Simplify and you'll be able to get your answer. ;)

Answer 7

Oh dear, the first time I did the problem I didn't multiply the 4x, but for some reason when I wrote it on here I had forgotten. Thank you for your help, but I have gotten to that point, and that is where the trouble starts. :/ I'll try working with it again, though.

Answer 8

Sorry a little typing mistake:
1=(x-2)/(x-2) eqn2