Question

Сократи дробь x^2−4/x^2+4x−12. Получаем дробь: x x (знак действия вводи в отдельное окошечко).

Answer 1

$\displaystyle \tt \frac{x^{2}-4}{x^{2}+4x-12}=\frac{(x-2)(x+2)}{(x-2)(x+6)}=\frac{x+2}{x+6};\\\\\\x^{2}+4x-12=0 \ \ \ \ \ \ \ \ \ D=b^{2}-4ac=4^{2}-4\cdot(-12)=16+48=64\\\\x_{1,2}=\frac{-bб\sqrt{D}}{2a}\\\\x_{1}=\frac{-4+8}{2}=2\\\\x_{2}=\frac{-4-8}{2}=-6\\\\\\x^{2}+4x-12=a(x-x_{1})(x-x_{2})=(x-2)(x+6)$

Answer 2

$\frac{x {}^{2} - 4}{x {}^{2} + 4x - 12 } = \frac{(x - 2)(x + 2)}{(x + 6)(x - 2)} = \frac{x + 2}{x + 6}$