The numerator of these algebraic fractions must be factored. The denominator is one of those factors. A simple comparison is needed. If a numerator is factored into 2*5 and the denominator is 2, the 2's "cancel" each other and the final answer is 5. That same concept will apply to these fractions.
(x² - x - 6)/x - 3 becomes (x + 2)(x - 3)/(x - 3) Answer: x + 2
(x² - 36)/x + 6 becomes (x - 6)(x + 6)/(x + 6) Answer: x - 6
(x² - 5x - 24)/x + 3 becomes (x - 8)(x + 3)/(x + 3) Answer: x - 8
Factor and simplify these algebraic fractions. Strive to be able to accomplish the problems with ease and then strive to increase your speed. Good luck and enjoy the challenge!