Rearrange an Algebraic Equation

I would like to rearrange the equation:

X = (Y-A)/(Y-B) to look like this

B-A = ((X-1)*(Y-A))/X

I'm able to isolate B-A on the left hand side of the equation, but I

can't seem to get the right hand side to the form above.

I've tried the following steps:

1. XY-XB = Y-A

2. XY-XB-Y = -A

3. XY-Y = XB-A

4. XY-Y = X(B-(A/X))

5. (XY-Y)/X = B-(A/X)

6. B = (XY-Y)/X + (A/X) = (XY-Y+A)/X

7. B-A = ((XY-Y+A)/X)-A

and this is where I get stuck. I feel like I'm close but I can't

quite get it in the form shown above. What am I missing?

Thanks.