How to find LCD?

Question

Hi, how do I find the LCD of : 1—2/3 - 3x+2/3x-3

 

It says the answer is 3(x-1) but I have no idea how to get to the answer

Answer 1

2/3 - (3x+2)/(3x-3)

 

= 2/3 - (3x+2)/3(x-1)

 

The first denominator is 3

The 2nd denominator is 3(x-1)

The LCD ... smallest thing that both 3 and 3(x-1)

divide into... is 3(x-1).

 

Multiply 2/3 by (x-1)/(x-1)

 

2(x-1)/3(x-1) - (3x+2)/3(x-1)

 

= (2x-2 - 3x -2)/3(x-1)

= (-x-4)/3(x-1)