Answer:
To simplify the expression \(\frac{x}{2} ÷ \frac{x+4}{14}\), you can use the following steps:
1. Rewrite the division as multiplication by the reciprocal of the second fraction:
\(\frac{x}{2} \cdot \frac{14}{x+4}\)
2. Cancel out common factors between the numerators and denominators:
\(x\) and \(x+4\) do not have any common factors that can be canceled.
3. Multiply the numerators and denominators together:
\(x \cdot 14\) in the numerator and \(2 \cdot (x+4)\) in the denominator:
\(\frac{x \cdot 14}{2 \cdot (x+4)}\)
4. Simplify further:
\(x \cdot 14\) is the same as \(14x\), and \(2 \cdot (x+4)\) is the same as \(2x + 8\):
\(\frac{14x}{2x + 8}\)
Now, the expression is in its simplest form: \(\frac{14x}{2x + 8}\).
Explanation: