Exploring Domains in Rational Fractions: (4/(x-2))×(7x/(x-6))=2

Determine the area of the domain without solving the expression:

$(\frac{4}{x-2})\times(\frac{7x}{x-6})=2$

To solve this problem, we'll determine where the given expression is undefined:

• Step 1: Identify where the first fraction, $\frac{4}{x-2}$, is undefined. This fraction is undefined when its denominator is zero: $x-2 = 0$. Thus, $x = 2$.
• Step 2: Identify where the second fraction, $\frac{7x}{x-6}$, is undefined. This fraction is undefined when its denominator is zero: $x-6 = 0$. Thus, $x = 6$.
• Step 3: The expression is undefined at $x = 2$ and $x = 6$.

Therefore, the domain of the expression excludes $x = 2$ and $x = 6$.

The correct domain restriction is $x \neq 2, x \neq 6$.