Вправи 401 - 467 » 403 (7-12)

7) (1 + b)–1 – (1 + b)–2 = 1^(\1+b)/(1+b) – 1/〖(1+b)〗^2 = (1+b -1)/〖(1+b)〗^2 = b/〖(1+b)〗^2 ; 8) (m + n)–1 – (m + n)–2 = 1^(\m+n)/(m+n) – 1/〖(m+n)〗^2 = (m+n-1)/〖(m+n)〗^2 ; 9) mn(m2 – 1)–1 – ((m-1)/n)–1 = mn/(m^2- 1) – n/(m-1) = mn/(m-1)(m+1) – n^(\m+1)/(m-1) = (mn-mn-n)/((m-1)(m+1)) = –n/(m^2- 1) = n/〖1-m〗^(2 ) ; 10) 1 – (1 + x–1)–1 = 1 – 1/(1+ 1/x) = 1 – 1/((x+1)/x) = 1\x+1 – x/(x+1) = (x+1-x)/(x+1) = 1/(x+1); 11) (1 + (1 + a–1)–1)–1 = (1 + (1 + 1/a)–1)–1 = (1 + ((a+1)/a)–1)–1 = (1 + a/(a+1))–1 = ((a+1+a)/(a+1))–1 = ((2a+1)/(a+1))–1 = (a+1)/(2a+1); 12) (a – a–1)–2 + (1 – a2)–2 = (a – 1/a)–2 + 1/((〖1-a〗^2 )^2 ) = ((a^2- 1)/a)–2 + 1/(〖(1-a〗^2 )^2 ) = (a/(a^2- 1))2 + 1/(〖(a〗^2- 1)^2 ) = a^2/(〖(a〗^2- 1)^2 ) + 1/(〖(a〗^2- 1)^2 ) = (a^2+ 1)/(〖(a〗^2- 1)^2 ).