is (12x/ x-1) -(12/x-1) = x/x-1 or 12? and y ?

Question

thanks so much for your help

Answer 1

(12x/ x-1) -(12/x-1) =
[12x - 12] / (x-1) =
12(x-1) / (x-1) =
12


Explanation.

{line1}: the two fractions, (12x/ x-1) and (12/x-1) have the same denominator, so you can take both numerators over the same fraction line as we have done in the {line2}

{line2}:
12x - 12
Factor out 12
12x - 12 = 12·(x-1)

{line3}:
(x-1) is a factor in the denominator as well as in the numerator -> they cancel out:
12(x-1) / (x-1) = 12·1 / 1 = 12

Hope this helps!

Answer 2

If the bar line in each fraction puts x - 1 on the bottom:
12x / (x - 1) - 12 / (x - 1)
= (12x - 12) / (x - 1)
= 12(x - 1) / (x - 1)
= 12.

If the question is really as you have written it, it would be interpreted as:
(12x / x) - 1 - [ (12/x) - 1 ]
= 12 - 1 - (12/x) + 1
= 12 - (12/x)
= (12x - 12) / x
= 12(x - 1) / x.

It looks as though the first option was the one you wanted.

Answer 3

12x/x-1 -12/x-1
use x-1 as the lcd
12x-12/x-1
12(x-1)/x-1
x-1 cancel out
x=12