SOLUTION: If a/b = c/d = k Find the value of (3a^2-ac+c^2)/(3b^2-bd+d2) in terms of k. a/b=k;i.e a=bk, c/d=k, i.e c=dk.

Algebra ->  Equations -> SOLUTION: If a/b = c/d = k Find the value of (3a^2-ac+c^2)/(3b^2-bd+d2) in terms of k. a/b=k;i.e a=bk, c/d=k, i.e c=dk.       Log On


   

Question 1115972: If a/b = c/d = k
Find the value of (3a^2-ac+c^2)/(3b^2-bd+d2) in terms of k. a/b=k;i.e a=bk, c/d=k, i.e c=dk.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find the value of %283a%5E2-ac%2Bc%5E2%29%2F%283b%5E2-bd%2Bd2%29 in terms of k. a/b=k;i.e a=bk, c/d=k, i.e c=dk.
In the numerator, replace a with bk, replace c with with dk
3%28bk%29%5E2+-+%28bk%29%28dk%29+%2B+%28dk%29%5E2
3b%5E2k%5E2+-+bdk%5E2+%2B+d%5E2k%5E2
Factor out k^2
k%5E2%283b%5E2+-+bd+%2B+d%5E2%29
with the denominator
k%5E2%283b%5E2+-+bd+%2B+d%5E2%29%2F%283b%5E2-bd%2Bd%5E2%29
fraction cancels, left with
k%5E2; k = 1