To solve for \( d \) in the equation
\[ \frac{d-2}{d-3} = \frac{1}{-m}, \]
we'll first eliminate the fractions by cross-multiplying:
\[ (d - 2)(-m) = (d - 3)(1). \]
Expanding both sides gives:
\[ -m(d - 2) = d - 3. \]
Distributing on the left side:
\[ -md + 2m = d - 3. \]
Next, we can rearrange the terms to isolate \( d \). First, add \( md \) to both sides and add 3 to both sides:
\[ 2m + 3 = d + md. \]
Factoring out \( d \) on the right side:
\[ 2m + 3 = d(1 + m). \]
Now, we can solve for \( d \) by dividing both sides by \( 1 + m \):
\[ d = \frac{2m + 3}{1 + m}. \]
Thus, the solution for \( d \) is:
\[ \boxed{\frac{2m + 3}{1 + m}}. \]