Question

упростите выражение:
а)

$frac{a {}^{2} - 2a + 1 }{(a - frac{ 1}{a}) {}^{2} }$
b)
$frac{m {}^{2} - 4m + 4 }{(m - frac{4}{m} ) {}^{2} }$

Answer 1

a)
(a²-2a+1)/(a-1/a)²=(a-1)²/((a²-1)²/a²)=(a-1)²/((a-1)²(a+1)²/a²)=a²/(a+1)²=(a/(a+1))²
b)
(m²-4m+4)/(m-4/m)²=(m-2)²/((m²-4)/m)²=(m-2)²/((m-2)²((m+2)²/m²)=
=m²/(m+2)²=(m*(m+2))².