Вправи 401 - 467 » 410

410. Спростіть вираз: 1) (m^2/(m^2-1))–1 • ((m+1)/m)–1 = (m^2-1)/m^2 • m/(m+1) = ((m-1)(m+1))/m^2 • m/(m+1) = (m-1)/m. 2) (n/m)–1 – (m/n)–1 = m/n – n/m = (m^2-n^2 )/mn; 3) (x^(-1)+x^(-2)+ x^(-3) )/(x+ x^2+ x^3 ) = (1/x+ 1/x^2 +1/x^3 )/(x+x^2+x^3 ) = ((x^2+ x+1)/x^3 )/(〖x(1+ x+ x〗^2)) = (x^2+ x+1)/(x^3• x(1+ x+x^2) ) = 1/x^4 = x–4; 4) (〖mn〗^(-6)+m^(-2) )/(m^3 n^(-8)+ n^(-2) ) = (m^(-2) (m^(1-(-2)) n^(-6)+1))/(n^(-2) (m^3 n^(-8-(-2) )+1)) = (m^(-3) (m^3 n^(-6)+1))/(n^(-2) (m^3 n^(-6)+1)) = (m/n)–2 = (n/m)2.