Given that \(\frac{a}{b} = \frac{c}{d} = k\) we can express \(a\) and \(c\) as: \(a = kb, \quad c = kd\) We want to find the value of \(\frac{3a^2 - ac + c^2}{3b^2 - bd + d^2}\) Substituting \(a\) and \(c\) into the expression gives: \(3a^2 - ac + c^2 = 3k^2b^2 - k^2bd + k^2d^2 = k^2(3b^2 - bd + d^2)\) Thus, the expression simplifies to: \(\frac{k^2(3b^2 - bd + d^2)}{3b^2 - bd + d^2} = k^2\) Therefore, the value is: \(k^2\)