1. **State the problem:** Simplify the expression $$\frac{3y}{y^2 + 3y - 10} - \frac{5}{2y + 10}$$ and check if it equals $$\frac{5y - 5}{y^2 + 3y - 10}$$. 2. **Factor the denominators:** - Factor $$y^2 + 3y - 10$$: $$y^2 + 3y - 10 = (y + 5)(y - 2)$$ - Factor $$2y + 10$$: $$2y + 10 = 2(y + 5)$$ 3. **Rewrite the expression with factored denominators:** $$\frac{3y}{(y + 5)(y - 2)} - \frac{5}{2(y + 5)}$$ 4. **Find common denominator:** The least common denominator (LCD) is $$2(y + 5)(y - 2)$$. 5. **Rewrite each fraction with the LCD:** $$\frac{3y \cdot 2}{2(y + 5)(y - 2)} - \frac{5(y - 2)}{2(y + 5)(y - 2)}$$ 6. **Simplify numerators:** $$\frac{6y}{2(y + 5)(y - 2)} - \frac{5y - 10}{2(y + 5)(y - 2)}$$ 7. **Combine the fractions:** $$\frac{6y - (5y - 10)}{2(y + 5)(y - 2)} = \frac{6y - 5y + 10}{2(y + 5)(y - 2)} = \frac{y + 10}{2(y + 5)(y - 2)}$$ 8. **Factor numerator if possible:** $$y + 10 = (y + 5) + 5$$ (no common factor with denominator) 9. **Check if this equals the given option:** Given option is $$\frac{5y - 5}{y^2 + 3y - 10} = \frac{5(y - 1)}{(y + 5)(y - 2)}$$. 10. **Compare simplified expression and option:** Our simplified expression is $$\frac{y + 10}{2(y + 5)(y - 2)}$$, which is not equal to $$\frac{5(y - 1)}{(y + 5)(y - 2)}$$. **Final answer:** The simplified form of the original expression is $$\boxed{\frac{y + 10}{2(y + 5)(y - 2)}}$$, which is not the same as the given option $$\frac{5y - 5}{y^2 + 3y - 10}$$.