(11) 11. [G] Solve \( \frac{20}{x-4}=\frac{8}{x-2} \) for \( x \).

To solve the equation \( \frac{20}{x-4}=\frac{8}{x-2} \), first cross-multiply to eliminate the fractions: \( 20(x-2) = 8(x-4) \). Expanding both sides gives us \( 20x - 40 = 8x - 32 \). Next, isolate \( x \) by bringing the \( x \) terms to one side and the constants to the other: \( 20x - 8x = -32 + 40 \), which simplifies to \( 12x = 8 \). Dividing both sides by 12 gives \( x = \frac{2}{3} \). Now, let’s double-check: plugging \( x = \frac{2}{3} \) back into the original equation doesn’t work because it leads to division by zero in both fractions, which means we must also consider any extraneous solutions generated during the solving process. So, let’s mark \( x = \frac{2}{3} \) as not valid due to restrictions on the domain defined by \( x \neq 4 \) and \( x \neq 2 \).