Вправи 401 - 467 » 409 (1-3)

409. Спростіть вираз: 1) ((b^(-3)-1)/(b+1))–2 • ((2b+2)/(b^(-2)+b^(-1)+1 ))–2 = ((b+1)/(b^(-3)-1))2 • ((b^(-2)+b^(-1)+1 )/(2b+2))2 = 〖(b+1)〗^2/((1/b^3 -1)^2 ) • ((1/b^2 + 1/b+1)^2)/〖(2(b+1)〗^2 = (((1+ b+b^2)/b^2 )^2)/(4((1-b^3)/b^3 )^2 ) = (((1+ b+ b^2)/b^2 )^2 )/(4•(((1- b)(1+ b+b^2))/b^3 )^2 ) = (〖(1+ b+ b〗^2 )^2•〖(b〗^3 )^2 )/(〖(b〗^2 )^2•4• 〖(1- b)〗^2 〖(1+ b+ b〗^2 )^2 ) = b^2/〖4(1- b)〗^2 ; 2) (a(a/b)–2)–1 : ((a/b)–1b)2 = (a(b/a)2)–1 : (b/a • b)2 = (b^2/a)–1 : (b^2/a)2 = a/b^2 • a^2/b^4 = a^3/b^6 ; 3) ((n/m)–2 – (m/n)–2) • (mn)2 = ((m/n)2 – (n/m)2) • (mn)2 = (m^2/n^2 – n^2/m^2 ) • m2n2 = m4 – n4;