If (2t - 3s)(t - s) = 0, find \(\frac{t}{s}\)

A.

\(\frac{3}{2}\) or \(1\)

B.

\(\frac{3}{2}\) or \(-1\)

C.

\(\frac{-3}{2}\) or \(-1\)

D.

\(\frac{-3}{2}\) or \(1\)

Correct answer is A

\((2t - 3s)(t - s) = 0 \implies (2t - 3s) = \text{0 or} (t - s) = 0\)

\(2t - 3s = 0 \implies 2t = 3s \therefore \frac{t}{s} = \frac{3}{2}\)

\(t - s = 0 \implies t = s  \therefore  \frac{t}{s} = 1\)

\(\frac{t}{s} = \frac{3}{2} or 1\)