10. $\frac{6}{k - 1}=\frac{8}{k - 6}$

Explanation:

Step1: Cross - multiply

$6(k - 6)=8(k - 1)$

Step2: Expand both sides

$6k-36 = 8k - 8$

Step3: Move like terms to one side

$6k-8k=-8 + 36$

Step4: Simplify both sides

$-2k=28$

Step5: Solve for k

$k=-14$

Answer:

$k = - 14$