Question

Simplify and express the following as rational expression in lowest terms :​

Answer 1

Answer:

$\frac{ {x}^{2} + 2x - 24 }{ {x}^{2} - x - 12 } \div \frac{ {x}^{2} - x - 6 }{ {x}^{2} - 9} \\ = \frac{ {x}^{2} + 6x - 4x - 24}{ {x}^{2} - 4x + 3x - 12 } \div \frac{ {x}^{2} - 3x + 2x - 6}{(x + 3)(x - 3)} \\ = \frac{x(x + 6) - 4(x + 6)}{x(x - 4) + 3(x - 4)} \div \frac{x(x - 3) + 2(x - 3)}{(x + 3)(x - 3)} \\ = \frac{(x + 6)(x - 4)}{(x - 4)(x + 3)} \div \frac{(x - 3)(x + 2)}{(x - 3)(x + 3)} \\ = \frac{x + 6}{x + 3} \div \frac{x + 2}{x + 3} \\ = \frac{x + 6}{x + 3} \times \frac{x + 3}{x + 2 } \\ = \frac{x + 6}{x + 2}$