Question

Simplify: $\frac{x^2-4x-21}{x^2-9x+14}$

• A. $\frac{x+3}{x-2}$
• B. $\frac{x-3}{x+2}$
• C. $\frac{x-4}{x-3}$
• D. $\frac{x+7}{x-2}$

Answer 1

The correct option is A $\frac{x+3}{x-2}$

The value of $\frac{x^2-4x-21}{x^2-9x+14}$

$=\frac{x^2-7x+3x-21}{x^2-7x-2x+14}$

$=\frac{x(x-7)+3(x-7)}{x(x-7)-2(x-7)}$

$=\frac{(x-7)(x+3)}{(x-7)(x-2)}$

$=\frac{x+3}{x-2}$