A.[tex]\frac{x^{2} + x - 12}{x - 3} = \frac{x^{2} + 4x - 3x - 12}{x - 3} = \frac{x(x) + x(4) - 3(x) - 3(4)}{x - 3} = \frac{x(x + 4) - 3(x + 4)}{x - 3} = \frac{(x + 4)(x - 3)}{x - 3} = x + 4[/tex]
B.[tex]\frac{5x -25}{x^{2} - 3x - 10} = \frac{5(x) - 5(5)}{x^{2} - 5x + 2x - 10} = \frac{5(x - 5)}{x(x) - x(5) + 2(x) - 2(5)} = \frac{5(x - 5)}{x(x - 5) + 2(x - 5)} = \frac{5(x - 5)}{(x + 2)(x - 5)} = \frac{5}{x + 2}[/tex]
C.[tex]\frac{x^{2} - 16}{x^{2} + 2x - 24} = \frac{x^{2} + 4x - 4x - 16}{x^{2} + 6x - 4x - 24} = \frac{x(x) + x(4) - 4(x) - 4(2)}{x(x) + x(6) - 4(x) - 4(6)} = \frac{x(x + 4) - 4(x + 4)}{x(x + 6) - 4(x + 6)} = \frac{(x - 4)(x + 4)}{(x - 4)(x + 6)} = \frac{x + 4}{x + 6}[/tex]
