Question

solve for x using common denominators.
\frac{3}{5(x - 4)} = \frac{x}{(x - 4)}
options: \frac{5}{3}, \frac{5}{33}, \frac{3}{5}, \frac{3}{55}, \frac{3}{5}

Explanation:

Step1: Identify the common denominator

The denominators are \(5(x - 4)\) and \((x - 4)\). The common denominator is \(5(x - 4)\) (note that \(x
eq4\) to avoid division by zero).

Step2: Multiply both sides by the common denominator

Multiply each term by \(5(x - 4)\):

$$ \frac{3}{5(x - 4)}\times5(x - 4)=\frac{x}{(x - 4)}\times5(x - 4) $$

Simplify each term:
The left - hand side simplifies to \(3\) (the \(5(x - 4)\) terms cancel out), and the right - hand side: \(\frac{x}{(x - 4)}\times5(x - 4)=5x\) (the \((x - 4)\) terms cancel out). So we have the equation \(3 = 5x\).

Step3: Solve for \(x\)

Divide both sides of the equation \(3 = 5x\) by \(5\):
\(x=\frac{3}{5}\)

Answer:

\(\frac{3}{5}\) (assuming one of the options is \(\frac{3}{5}\), for example, if the option with \(\frac{3}{5}\) is labeled as, say, option C, then the answer would be C. \(\frac{3}{5}\))