Simplify the co 7) \( \frac{\frac{x}{3}-6}{10+\frac{4}{x}} \)

To simplify the expression \( \frac{\frac{x}{3}-6}{10+\frac{4}{x}} \), we can first find a common denominator for the numerator and the denominator. 1. **Numerator**: \(\frac{x}{3}-6\) - Convert \(6\) into a fraction with a denominator of \(3\): \[ 6 = \frac{18}{3} \] - Now it's: \[ \frac{x}{3} - \frac{18}{3} = \frac{x - 18}{3} \] 2. **Denominator**: \(10 + \frac{4}{x}\) - Convert \(10\) into a fraction with a denominator of \(x\): \[ 10 = \frac{10x}{x} \] - Now it's: \[ \frac{10x + 4}{x} \] Now, we can substitute these into the original expression: \[ \frac{\frac{x - 18}{3}}{\frac{10x + 4}{x}} \] To divide by a fraction, we multiply by its reciprocal: \[ \frac{x - 18}{3} \cdot \frac{x}{10x + 4} = \frac{x(x - 18)}{3(10x + 4)} \] So, the simplified form of the given expression is: \[ \frac{x(x - 18)}{3(10x + 4)} \] You can simplify further if needed depending on your specific conditions or values for \(x\)!