Simplify the expression. \[ \frac{2}{7+\sqrt{7}} \]

Step 1 ：The given expression is \(\frac{2}{7+\sqrt{7}}\).

Step 2 ：The denominator contains a square root. To simplify this expression, we need to rationalize the denominator.

Step 3 ：To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator, which is \(7 - \sqrt{7}\).

Step 4 ：After multiplying, the denominator becomes a difference of squares and simplifies to \(7^2 - (\sqrt{7})^2\), which is 49 - 7 = 42.

Step 5 ：The numerator becomes \(2(7 - \sqrt{7})\), which simplifies to \(14 - 2\sqrt{7}\).

Step 6 ：So, the expression becomes \(\frac{14 - 2\sqrt{7}}{42}\).

Step 7 ：We can simplify this further by dividing all terms by 2, resulting in \(\frac{7 - \sqrt{7}}{21}\).

Step 8 ：Finally, we can separate the fraction into two parts, resulting in \(\frac{1}{3} - \frac{\sqrt{7}}{21}\).

Step 9 ：Final Answer: The simplified expression is \(\boxed{\frac{1}{3} - \frac{\sqrt{7}}{21}}\)