Solve for \( x \) \[ \frac{-14}{x-3}=\frac{-8}{x} \]

To solve the equation: \[ \frac{-14}{x - 3} = \frac{-8}{x} \] follow these steps: 1. **Eliminate the Negative Signs:** Multiply both sides of the equation by \(-1\) to simplify: \[ \frac{14}{x - 3} = \frac{8}{x} \] 2. **Cross-Multiply to Eliminate the Fractions:** Multiply the numerator of one side by the denominator of the other side: \[ 14 \cdot x = 8 \cdot (x - 3) \] Simplifying gives: \[ 14x = 8x - 24 \] 3. **Isolate the Variable \( x \):** Subtract \(8x\) from both sides to gather like terms: \[ 14x - 8x = -24 \] \[ 6x = -24 \] 4. **Solve for \( x \):** Divide both sides by \(6\): \[ x = \frac{-24}{6} = -4 \] 5. **Check for Validity:** Ensure that the solution does not make any denominator zero: - If \( x = -4 \), then \( x - 3 = -4 - 3 = -7 \neq 0 \) - Also, \( x \) itself is \(-4 \neq 0\) Thus, \( x = -4 \) is a valid solution. **Final Answer:** \[ x = -4 \]