Question

HELP PLEASE Simplify the rational expression. State any excluded values. x^2-12x+35/x^2-3x-10

Answer 1

$\frac{{x}^{2} - 12x + 35 }{ {x}^{2} - 3x - 10 }$
Factorise both the term by splitting the mid term and you'll get


$\frac{ {x}^{2} - 5x - 7x + 35}{ {x}^{2} - 5x + 2x - 10 } \\ = \frac{x(x - 5) - 7(x - 5)}{x(x - 5) + 2(x - 5)} \\ = \frac{(x - 7)(x - 5)}{(x + 2)(x - 5)} \\ = \frac{x - 7}{x + 2}$