(35^2-67^2):(66^2-34^2)

To solve the expression \((35^2 - 67^2) : (66^2 - 34^2)\), we can use the difference of squares formula, which states that \(a^2 - b^2 = (a - b)(a + b)\).

1. Calculate \(35^2 - 67^2\):

   • This can be written as \((35 - 67)(35 + 67)\).
   • \(35 - 67 = -32\)
   • \(35 + 67 = 102\)
   • Thus, \(35^2 - 67^2 = -32 \times 102 = -3264\).

2. Calculate \(66^2 - 34^2\):

   • This can be written as \((66 - 34)(66 + 34)\).
   • \(66 - 34 = 32\)
   • \(66 + 34 = 100\)
   • Thus, \(66^2 - 34^2 = 32 \times 100 = 3200\).

Now we substitute these back into the original expression:

\[ (35^2 - 67^2) : (66^2 - 34^2) = \frac{-3264}{3200} \]

3. Simplifying \(-\frac{3264}{3200}\):
   • To simplify, divide both the numerator and the denominator by 64 (the greatest common divisor):
   • \(-\frac{3264 \div 64}{3200 \div 64} = -\frac{51}{50}\).

Thus, the final answer is:

\[ -\frac{51}{50} \]