Find Original Fraction

Tell me if the set up is right.

Numerator of original fraction = x - 8.
Denominator of original fraction = x.

Original Fraction = (x - 8)/x.

Numerator of new fraction = (x - 8) + 1 = (x - 7).
Denominator of new fraction = (x - 3).

Here is my set up:

(x - 7)/(x - 3) = 2/3

Yes?

 

correct

 

At least I can do the easy stuff. Some people can't even do that right.

 

(x - 7)/(x - 3) = 2/3

x=15
=>Original Fraction = (x - 8)/x=(15-8)/15=7/15

check:

(7+1)/(15-3)= 2/3

 

I got it right.

 

IF you first state that you are letting the denominator be "x" then you can say that the numerator is x- 8.

 

Ok. Noted.