solving equations?

Question

solve for x....
(5a/x) = (5b/x-1) and that is x -1

Answer 1

Multiply by x(x-1) to get rid of all the denominators:

5a/x = 5b/(x-1)
5a(x-1) = 5b(x)
5ax -5a = 5bx

Divide by 5, solve for x:

ax - a = bx
ax - bx = a
(a-b)x = a
x = a/(a-b)

Answer 2

5a(x-1)=5bx
5ax-5bx=5a
5(a-b)x=5a
(a-b)x=a
if a=b=0 => x are every real number without 0 and 1
if a=b but a is not "= " to 0 => x not exist
if a is not "= " to b => x=a/(a-b)

Answer 3

5a/x = 5b/(x-1)
5a(x-1) = 5bx
5ax-5 = 5bx
5ax - 5bx = 5
x(5a-5b) = 5
x = 5/(5a-5b) = 1/(a-b)