Question

Solve for D
d-2/d-3 = 1/-m

Answer 1

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:

\[
\boxed{\frac{2m + 3}{1 + m}}.
\]