Solve the Rational Equation: Isolate X in 5/(x-8) = 3/4x

To solve the equation $\frac{5}{x-8} = \frac{3}{4x}$ for the variable $x$, we will follow these steps:

Step 1: Apply cross-multiplication to the equation. This involves multiplying the numerator of each fraction by the denominator of the other fraction:

$5 \cdot 4x = 3 \cdot (x - 8)$

Step 2: Simplify both sides of the resulting equation:

$20x = 3x - 24$

Step 3: Rearrange the equation to isolate terms involving $x$ on one side:

$20x - 3x = -24$

This simplifies to:

$17x = -24$

Step 4: Solve for $x$ by dividing both sides of the equation by 17:

$x = \frac{-24}{17}$

Therefore, the solution to the equation is:

$x = \frac{-24}{17}$