Để giải phương trình này, ta cần tìm giá trị của \( x \) sao cho phương trình sau đúng:

\[ \frac{14}{3x-12} - \frac{2+x}{x-4} = \frac{3}{8-2x} - \frac{5}{6} \]

Bước 1: Đơn giản hóa các mẫu số để dễ dàng làm việc với phương trình.

\[ 3x - 12 = 3(x - 4) \]
\[ 8 - 2x = 2(4 - x) \]

Bước 2: Đưa tất cả các phân số về cùng mẫu số chung.

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

Bước 3: Tìm mẫu số chung cho các phân số.

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

Mẫu số chung của vế trái là \( 3(x-4) \) và của vế phải là \( 6(4-x) \).

Bước 4: Quy đồng mẫu số và giải phương trình.

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \frac{3}{2(4-x)} - \frac{5}{6} \]

\[ \frac{14}{3(x-4)} - \frac{2+x}{x-4} = \