Answer:
k = (3 x^2 - 3 x + 1)/(2 x^2 - 2 x)
Step-by-step explanation:
Solve for k:
1 + x (2 k - 3) + x^2 (3 - 2 k) = 0
Expand and collect in terms of k:
1 - 3 x + 3 x^2 + k (2 x - 2 x^2) = 0
Multiply both sides by -1:
-1 + 3 x - 3 x^2 + k (2 x^2 - 2 x) = 0
Subtract -3 x^2 + 3 x - 1 from both sides:
k (2 x^2 - 2 x) = 3 x^2 - 3 x + 1
Divide both sides by 2 x^2 - 2 x:
Answer: k = (3 x^2 - 3 x + 1)/(2 x^2 - 2 x)
