Вправа 301 - 400 » 337

337. Спростіть вираз. a) (n^2-1)/(n^2+ n) • (1 – 1/(1-1/n )) = (n^2-1)/(n^2+ n) • (1 – n/(n-1)) = (n^2-1)/(n^2+ n) • (n-1- n)/(n-1) = ((n+1)•(-1))/(n(n+1)) = –1/n; б) (a^4+c^4 )/〖(a- c)〗^2 – 2/((1/a-1/c )^2 ) = (a^4+c^4 )/〖(a- c)〗^2 – (〖2a〗^2 c^2)/〖(a- c)〗^2 = (a^4+c^4- 〖2a〗^2 c^2 )/〖(a- c)〗^2 = (〖(a〗^2-c^2 )^2)/〖(a- c)〗^2 = (〖(a- c)〗^2 〖(a+ c)〗^2)/〖(a- c)〗^2 = (a + c)2.