Solve for X: Complex Fraction Equation (8-3(x-2))/(5-x) = 4/3

We will solve the equation $\frac{8-3(x-2)}{5-x} = \frac{4}{3}$ step by step.

First, clear the fraction by multiplying both sides of the equation by $5-x$:

$8 - 3(x-2) = \frac{4}{3} \cdot (5-x)$

Distribute the $-3$ on the left side:

$8 - 3x + 6 = \frac{4}{3}(5-x)$

Combine like terms on the left side:

$14 - 3x = \frac{4}{3}(5-x)$

Now, clear the fraction on the right side by multiplying through by 3:

$3(14 - 3x) = 4(5-x)$

Distribute the values on both sides:

$42 - 9x = 20 - 4x$

Rearrange the equation to isolate terms with $x$:

$42 - 20 = 9x - 4x$

Simplify the equation:

$22 = 5x$

Solve for $x$ by dividing both sides by 5:

$x = \frac{22}{5}$

Therefore, the solution to the problem is $x = \frac{22}{5}$.