If a = 1, b = 3, solve for x in the equation \(\frac{a}{a - x}\) = \(\frac{b}{x - b}\)
A
\(\frac{4}{3}\)
B
\(\frac{2}{3}\)
C
\(\frac{3}{2}\)
D
\(\frac{3}{4}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\frac{a}{a - x}\) = \(\frac{b}{x - b}\)
\(\frac{1}{1 - x}\) = \(\frac{3}{x - 3}\)
∴ 3(1 - x) = x - 3
3 - 3x = x - 3
Rearrange 6 = 4x; x = \(\frac {6}{4}\)
= \(\frac{3}{2}\)
Source: Myschool Past Questions Archive (Record #31009)