Question

How do you solve `(x+2)/(x-2)=4/8`?

Answer 1

`x = -6`

Explanation:

First, we each side of the equation by a common denominator (in this case `8(x - 2)`) to eliminate the fraction and keep the equation balanced:

`8(x - 2) (x + 2)/(x - 2) = 8(x - 2) 4/8`

`8cancel((x - 2)) (x + 2)/cancel((x - 2)) = cancel(8)(x - 2) 4/cancel(8)`

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

Now we can expand the terms in parenthesis on each side of the equation:

`8x + 16 = 4x - 8`

Next we can isolate the `x` terms on one side of the equation and the constants on the other side of the equation while keeping the equation balanced:

`8x + 16 - 16 - 4x = 4x - 8 - 16 - 4x`

`8x + 0 - 4x = 0 - 24`

`8x - 4x = -24`

`4x = -24`

Finally, we can solve for `x` while keeping the equation balanced:

`(4x)/4 = (-24)/4`

`(cancel(4)x)/cancel(4) = -6`

`x = -6`