If \(\frac{a}{b}\) = \(\frac{c}{d}\) = k, find the value of \(\frac{3a^2 - ac + c^2}{3b^2 - bd + d^2}\) in terms of k
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: \(k^2\)
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