Question about this linear equation with fractions

[hackedagainanda]

Homework Statement

8/(x - 2) - (13/2) = 3/(2x - 4)

Relevant Equations

None.

I use 2x -4 as the LCD and turn 8/(x - 2) - (13/2) = 3 into 16 - 13x - 4 = 3, I then get 12 - 13x = 3 which leads me to 13x = -9 so x = -9/13 which is the wrong answer.

Where did I make a mistake?

 

[hackedagainanda]

I found my mistake, (-13/2) * 2x -4 is - 13(x - 2) = 13x + 26 so then its 16 + 26 = 42 + 13x = 3 and then 42 - 3 = 39 then 13x = 39 so x is 3.

 

[SammyS]

I found my mistake, (-13/2) * 2x -4 is - 13(x - 2) = 13x + 26 so then its 16 + 26 = 42 + 13x = 3 and then 42 - 3 = 39 then 13x = 39 so x is 3.

The solution may be x = 3, but you have several errors.

−13(x − 2) = −13x +26 .

That gives the Left Hand Side as being:
(2x − 4)(8/(x − 2) − (13/2)) which is 16 + 26 − 13x and finally 42 − 13x

The Right Hand Side becomes 3.

 

[hackedagainanda]

Thanks for the tip, I was sloppy when writing down the equation. I need to slow down and make sure all the signs are correct.