Algebra question for 10 points, best at showing steps #1!?

Question

I have 25 more homework problems like this one and the steps will give me the key to the other 23.

15/x - 15/x + 2 = 2

and

3x/x+2 - x/ x-2 + 8/ x squared - 4

I have been doing homework for 4 hours and am getting fried. Thanks in advance for the help!

sorry guys, the first should have read:

15/X - 15/(x+2) = 2

or

15 - 15 =2
__ __
x x+2

sorry guys, the first should have read:

15/X - 15/(x+2) = 2

or

15 - 15 =2
__ __
x x+2

Answer 1

In the first problem, the 15/x - 15/x cancels out, so the equation is true whenever x is not 0. x>0, x<0.

If there's a parenthesis around the (x+2), that's different.
15/x - 15/(x+2) = 2
Multiply everything by x(x+2)
15x(x+2)/x - 15x(x+2)/(x=2) = 2x(x+2)
15(x+2) - 15x = 2x(x+2)
15x +30 -15x = 2x^2 +2x
0 = 2x^2 +2x -30
0 = x^2 +x -15
You should be able to get it from there.

Second one, assuming the parentheses are missing?
3x/(x+2) - x/(x-2) +8/(x^2 -4) = something (zero?)
Multiply everything by (x^2-4)
3x(x^2-4)/(x+2) - x(x^2-4)/(x-2) + 8(x^2-4)/(x^2-4) = 0
Recall x^2 -4 = (x+2)(x-2)
So factoring
3x(x+2)(x-2)/(x+2) - x(x+2)(x-2)/(x-2) +8 = 0
3x(x-2) - x(x+2) +8 = 0
3x^2 -2x -x^2 -2x +8 = 0
2x^2 -4x +8 = 0
x^2 - 2x +4 = 0
Should be able to get home from there.

Answer 2

The first is a little odd, because the fractions already have common denominators and when added together become zero. So you have 2 = 2 which is true for all x (leaving out 0 because you can't have 0 in the bottom of a fraction.

The second one is harder. You have to factor by FOIL the third denominator to be (x+2)(x-2)

Since the first fraction already has the (x+2), multiply top & bottom by (x-2) to get 3x(x-2) over (x+2)(x-2)
or
3x^2 - 6x over (x+2)(x-2)

The second already has the (x-2) so multiply top & bottom by (x+2) to get -x(x+2) over (x+2)(x-2)
or
-x^2 - 2x over you know what

Leave the third fraction alone since it already has the C.D.

Now combine all the like terms on top:

3x^2 + 6x - x^2 - 2x + 8
= 2x^2 - 4x + 8
= 2(x^2 - 2x + 4) all over (x+2)(x-2)

Answer 3

15/x + 15/x +2 = 2

Multiply both sides by x to give
15 + 15 + 2 = 2x
which =
32 = 2x
which means x is 16

3x / x+2 - x / x-2 + 8 / x^2 -4 - whats on the other side of the equation for this one?