algebra help?

Question

1 / x+2 + 2 / x-2 = 1 / x2 - 4

Answer 1

So you want to solve

1/(x+2) + 2/(x-2) = 1/(x^2 - 4)

Your first step is to note that x^2 - 4 = (x+2)(x-2)

1/(x+2) + 2/(x-2) = 1/[(x+2)(x-2)]

Next, you multiply both sides by the lowest common denominator; by inspection, we can see that it is (x+2)(x-2). Note that the purpose of multiplying by the LCD is to eliminate all fractions, and that's exactly what happens.

1(x-2) + 2(x+2) = 1

Solve as normal.

x - 2 + 2x + 4 = 1
3x + 2 = 1
3x = -1
x = -1/3

Answer 2

Hey, firstly you should have put brackets cause it kinda looks confusing....p.s. don't forget that for the exam...
secondly,is your question 1/(x+2) +2/(x-2)=1/(x^2) - 4
well you have to cross multiply the left hand side first ok and on the right hand side too...this will end up as ((x-2)+2(x+2))/(x+2)(x-2) =(1-4x^2)/x^2.....remember when you cross multiply it is like if...say the number is 4, it is really 4/1 okay..
then, you expand you will end up with (x-2+2x+4)/((x+2)(x-2) =(1-4x^2)/x^2.

then,you are gonna cross multiply again, yes again...you will get,
(x^3-2x^2+2x^3+4x^2)/x^2(x+2)(x-2)....focusing on the denominator here...that will becomex^2(x^2-4).
so the question boils down to (x^3-2x^2+2x^3+4x^2)/x^2(x^2-4)

so you will minus and add like constants so it will end up as (3x^3+2X^2)/x^2(x^2-4)

then you factorise the numerator and this will be x^2(3x+2)/x^2(x^2-4)
the x^2 will cancel out and it is gonna take the form of 3x+2/x^2-4

you cross multiply...3x+2=x^2-4.
transposing, that's going to be x^2-3X-6=0

and you solve like normal...wait a second..it can't be solved you will have to use the formula...a^2+bx+c..that is put it in that form and use the formula...-b+ or - the square root of 4ac...all over 2a...

I know,it looks alittle hard but it is going to work out and i hope it helps...dont give up...i just hope you copied down the right question...

Answer 3

you need parenthesis, otherwise it is written like this;

1/x + 2/x +2 -2 = 1/x^2? -4

I think you mean;

1/(x+2) + 2/(x-2) = 1/(x^2-4)
1/(x+2) + 2/(x-2) = 1/((x+2)(x-2))

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

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

2+(x-2) = 1

x = 1

Answer 4

(x-2+2x+4)/(x^2-4)=1/(x^2-4)
or (3x+2)/(x^2-4)=1/(x^2-4)
or 3x+2=1
or 3x= -1
or x=-1/3
solved.

Answer 5

x =
3 x2
- ---------
4 x2 - 1

Answer 6

1/x+2+2/x-2=1/2x-4
(1+2x)/x+2/x-2=1/2x-4
(1+2x+2)/x-2=1/2x-4
(1+2x+2-2x)/x=1/2x-4
3/x=(1-8x)/2x
6=1-8x
6-1=-8x
5=-8x
x=-8/5
i think this will be the answer.i am not sure