Final answer:
To make x the subject of the formula, we start by eliminating the denominators through cross-multiplication. Then we simplify the equation and isolate the variable x. Finally, we factor out the x term and solve for x.
Step-by-step explanation:
To make x the subject of the formula a/a-x=b/b-x, we can start by cross-multiplying to eliminate the denominators.
This gives us a(b - x) = b(a - x). Next, we can distribute and simplify the equation to ab - ax = ab - bx.
Then, we can combine like terms and isolate the variable x. By subtracting bx from both sides of the equation, we get ab - ax - bx = ab - bx - bx.
Simplifying further, we have ab - ax - bx = ab - 2bx. Finally, we can factor out the x term on the left side and solve for x, which yields x = (ab - ab)/(a + 2b).