### Instruction: Evaluate $\dfrac{7}{45^2 - 38^2}$.### Response: This problem involves some large numbers, but I can simplify it by using the difference of squares formula: $a^2 - b^2 = (a + b)(a - b)$.
In this case, $a = 45$ and $b = 38$, so I can rewrite the denominator as $(45 + 38)(45 - 38)$.
This gives me $\dfrac{7}{(83)(7)}$.
Now I can cancel out the common factor of 7 in the numerator and the denominator, and get $\dfrac{1}{83}$.