Help solving a math equation!?

Question

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

Answer 1

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

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

4-2x = (x-2)(x+2)

4-2x = x²-4

x²+2x-8=0

(x+4)(x-2) = 0

x+4=0
x=-4

x-2=0
x=2

Answer 2

Problem:
4 - 2X
-------- = X - 2
X + 2

1) Cross Multiply.
4 - 2X * 1
Since there is no denominator under X-2, the denominator is automatically 1

(X-2) * (X+2)

When you multiply 4 - 2X * 1 you get 4 - 2X.

When you multiply (X - 2)(X+2) you must foil.
The result is:
x^2 -4

2) Set the two resulting answers equal to one another.

X^2 - 4 = 4 - 2X

3) Normally I would say move all X's to one side of the equation. However, since we have an X^2, I can see we ought to move everything over to one side and set it equal to 0.

Thus, I will move -2X and 4 to the left side of the equation by adding 2X to both sides and subtracting 4 from both sides, as these two moves cause the numbers to cancel on the right. The result is as follows:

X^2 + 2X -8 = 0

4) Factor:

(X + 4) (X - 2) = 0

5) Set each factor equal to 0 and solve:

X + 4 = 0
X = -4

X - 2 = 0
X = 2

6) Your answers are that X = 2 and -4. Going back to the original equation we try the answers to see if they are correct.

You will see that both solutions work.

Answer 3

4-2x ............ x-2
---------...=
x+2

cross multiply

4 - 2x = (x+2)(x-2)
4 - 2x = x^2 - 4
subtract 4 - 2x from both sides
0 = x^2 - 4 - 4 + 2x
0 = x^2 + 2x - 8
rewrite it with the zero on the right side
x^2 + 2x - 8 = 0
factor it out
(x+4)(x-2) = 0
x+4 = 0; x = -4
x-2 = 0; x = 2

then you have to make sure both of those answers dont give you a zero denominator (x+2 cannot equal zero)

2+2=4: -4+2=2
these are both nonzero so we are fine
answer; x=2, x = -4

Answer 4

I think the answer should be x^2 + 2x - 8 or (x+4)(x-2)

(the x^2 is x squared)

Answer 5

4-2x = x^2-4
0=x^2+2x-8
=(x+4)(x-2)
x=-4 or x =2

Answer 6

(4-2x) = (x-2)(x+2)
(4-2x)=x^2-4
x^2+2x-8=0
x=2 or -4

Answer 7

((4-2x)/(x+2)) = x-2
(-2*(x-2)/(x+2))=x-2
x+2=-2 (divide out (x-2) on each side)
x=-4