Add. (5)/(x+3)+(6)/(x-2) Simplify your answer as much as possible. square III

To simplify the expression $\frac{5}{x+3} + \frac{6}{x-2}$, we need to find a common denominator for the two fractions. The common denominator is the product of the two denominators, which is $(x+3)(x-2)$.<br /><br />Step 1: Rewrite each fraction with the common denominator.<br />$\frac{5}{x+3} + \frac{6}{x-2} = \frac{5(x-2)}{(x+3)(x-2)} + \frac{6(x+3)}{(x+3)(x-2)}$<br /><br />Step 2: Combine the fractions.<br />$\frac{5(x-2)}{(x+3)(x-2)} + \frac{6(x+3)}{(x+3)(x-2)} = \frac{5(x-2) + 6(x+3)}{(x+3)(x-2)}$<br /><br />Step 3: Simplify the numerator.<br />$5(x-2) + 6(x+3) = 5x - 10 + 6x + 18 = 11x + 8$<br /><br />Step 4: Write the final simplified expression.<br />$\frac{11x + 8}{(x+3)(x-2)}$<br /><br />Therefore, the simplified expression is $\frac{11x + 8}{(x+3)(x-2)}$.