Question

Сократите дробь:
a^2-4/a^2-6a+8

Answer 1

$\frac{a^{2}-4 }{a^{2}-6a+8 } =$

____________________________

a²-4 = a² -2² = (a-2)*(a+2)

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a²-6a+8 = 0

D = (-6)² - 4 * 8 = 36 - 32 = 4 = 2²

$a_{1} = \frac{6+2}{2} = 4$

$a_{1} = \frac{6-2}{2} = 2$

a²-6a+8 = (a-4)*(a-2)

____________________________

$= \frac{(a-2)(a+2)}{(a-4)*(a-2)} = \frac{a+2}{a-4}$

Answer 2

$\frac{a^{2}-4 }{a^{2}-6a+8 }=\frac{(a-2)(a+2)}{(a-2)(a-4)}=\frac{a+2}{a-4}\\\\Otvet:\boxed{\frac{a+2}{a-4}}$