Add or subtract as indicated and simplify if possible.
\[
\frac{-2 y}{2 y^{2}+5 y}+\frac{y-3}{2 y^{2}+y-10}
\]
Select one:
a. $\frac{1-y}{(2 y+5)(y-2)}$
b. $\frac{-2 y^{2}+y-3}{2 y^{3}+5 y^{2}-10}$
c. $\frac{-3 y^{2}+y+1}{y(2 y+5)(y-2)}$
d. $\frac{-y-3}{4 y^{2}+6 y-10}$
Answer
\(\boxed{\frac{1-y}{(2 y+5)(y-2)}}\) is the final answer.
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.
