Question

БУДЬ ЛАСКА ЦЕ ТЕРМІНОВО, ДАЮ 50 БАЛІВ​

Answer 1

Пояснення:

a)

$\displaystyle\\\frac{a+2}{a^2-2a+1}:\frac{a^2-4}{a-1} -\frac{1}{a-2}\\\\ 1)\ \frac{a+2}{a^2-2a+1}:\frac{a^2-4}{a-1} =\frac{a+2}{(a-1)^2} *\frac{a-1}{a^2-4}=\frac{a+2}{(a-1)^2} *\frac{a-1}{a^2-2^2}=\\\\ =\frac{a+2}{(a-1)^2} *\frac{a-1}{(a+2)*(a-2)}=\frac{(a+2)*(a-1)}{(a-1)^2*(a+2)*(a-1)}=\frac{1}{(a-1)*(a-2)}.$

$\displaystyle\\ 2)\ \frac{1}{(a-1)*(a-2)}-\frac{1}{a-2} =\frac{1-(a-1)}{(a-1)*(a-2)}=\frac{1-a+1}{(a-1)*(a-2)}=\\\\ =\frac{-a+2}{(a-1)*(a-2)}=\frac{-(a-2)}{(a-1)*(a-2)}=-\frac{1}{a-1} =\frac{1}{1-a}.$