Question

Question #939a5

Answer 1

`x = 4`

Explanation:

We need to remember that `a/b = c/d => ad = bc`

We can rewrite the equation as: `2(2x+4) = 12(x-2)`

`=> 4x + 8 = 12x - 24 => 8x = 32 => x = 4`

Normally, we would also take the restrictions `x != +-2` to make sure no denominator was zero, but this solution is fine.

Answer 2

`x=4`

Explanation:

Given: `color(red)(12/(2x+4))=color(blue)(2/(x-2))`
Note that the given expression is meaningless unless `x!=-2` and `x!=2`
... so we will make the assumption that these conditions have been met.

`color(red)(12/(2x+4)) * (x-2)/(x-2) = color(blue)(2/(x-2)) * (2x+4)/(2x+4)`

`color(green)((12x-24))/color(magenta)((2x+4) * (x-2)) = color(brown)((4x +8))/color(magenta)((2x+4) * (x-2))`

`color(green)(12x-24)=color(brown)(4x+8)`

`8x=32`

`x=4`