Question 5 $$ \begin{array}{l}\text { Add and, if possible, simplify: } \frac{y^{2}+7 y}{y^{2}-5 y}+\frac{y^{2}-4 y}{y^{2}-5 y} \ \text { OB. } \frac{2 y+3}{y-5} \ \text { O. } \frac{2 y^{2}+11}{y^{2}-5 y} \ \text { O. }-1\end{array} $$

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1. Write the given expression:
   $$
   \frac{y^{2}+7y}{y^{2}-5y} + \frac{y^{2}-4y}{y^{2}-5y}
   $$

2. Since the denominators are the same, combine the numerators:
   $$
   \frac{(y^{2}+7y) + (y^{2}-4y)}{y^{2}-5y}
   $$

3. Simplify the numerator:
   $$
   y^{2}+7y+y^{2}-4y = 2y^{2}+3y
   $$
   So the expression becomes:
   $$
   \frac{2y^{2}+3y}{y^{2}-5y}
   $$

4. Factor the numerator and the denominator:
   $$
   \text{Numerator: } 2y^{2}+3y = y(2y+3)
   $$
   $$
   \text{Denominator: } y^{2}-5y = y(y-5)
   $$

5. Cancel the common factor $$ y $$ (assuming $$ y \neq 0 $$):
   $$
   \frac{y(2y+3)}{y(y-5)} = \frac{2y+3}{y-5}
   $$

6. The simplified expression is:
   $$
   \frac{2y+3}{y-5}
   $$
The simplified expression is $$ \frac{2y+3}{y-5} $$.

Question 5

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