Step 1 :The given expressions are \(\frac{-2 y}{2 y^{2}+5 y}\) and \(\frac{y-3}{2 y^{2}+y-10}\).
Step 2 :To add these fractions, we need a common denominator. In this case, the denominators are already the same.
Step 3 :So, we can directly add the numerators. The result is \(-2y + y - 3\).
Step 4 :Simplify the numerator to get \(1 - y\).
Step 5 :So, the simplified form of the given expression is \(\frac{1-y}{(2 y+5)(y-2)}\).
Step 6 :\(\boxed{\frac{1-y}{(2 y+5)(y-2)}}\) is the final answer.