To evaluate the expression given \( h = -10 \) and \( j = 0 \), we can substitute these values into the expression:
\[ \frac{hj}{h + j} \]
First, we calculate \( hj \):
\[ hj = (-10)(0) = 0 \]
Next, we calculate \( h + j \):
\[ h + j = -10 + 0 = -10 \]
Now we can substitute these results back into the expression:
\[ \frac{hj}{h + j} = \frac{0}{-10} \]
Since any number divided by a non-zero number is 0, we have:
\[ \frac{0}{-10} = 0 \]
Thus, the simplified answer is:
\[ \boxed{0} \]