To find \( y \) when \( x = -3 \) for the equation

\[ y = \frac{x}{x-3} + \frac{x}{x+4}, \]

substitute \( x = -3 \) into the equation:

1. Substitute \( x = -3 \) into each term:

\[
\frac{-3}{-3 - 3} + \frac{-3}{-3 + 4}
\]

2. Simplify each term:

For the first term:
\[
\frac{-3}{-6} = \frac{1}{2}
\]

For the second term:
\[
\frac{-3}{1} = -3
\]

3. Add the two terms together:

\[
\frac{1}{2} - 3
\]

To subtract, convert \(-3\) to a fraction with the same denominator:

\[
-3 = -\frac{6}{2}
\]

So:

\[
\frac{1}{2} - \frac{6}{2} = -\frac{5}{2}
\]

Therefore, the value of \( y \) when \( x = -3 \) is:

D. \(-\frac{5}{2}\)