Problem

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. $\frac{-y-3}{4 y^{2}+6 y-10}$

Solution

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.

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Source: https://solvelyapp.com/problems/xmGG8XLyWy/

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