Вправи 201 - 342 » 281

281. Спростіть вираз: 1) (х–2 – 1)2 – (x–2 – 4)(х–2 + 4) = x–4 – 2х–2 + 1 – (х–4 – 16) = х–4 – 2х–2 + 1 – x–4 + 16 = –2х–2 + 17; 2) (a^(-2)- 10a^(-1) b^(-1)+ 25b^(-2))/(a^(-1)- 5b^(-1) ) = ((a^(-1) )^2- 2a^(-1) •5b^(-1)+ (5b^(-1) )^2)/(a^(-1)- 5b^(-1) ) = ((a^(-1)- 5b^(-1) )^2)/(a^(-1)- 5b^(-1) ) = a–1 – 5b–1; 3) (5m^(-2)+ n^(-2))/(4m^(-3)+ 4m^(-1) n^(-2) ) – m^(-1)/(m^(-2)+ n^(-2) ) = (5m^(-2)+ n^(-2))/(4m^(-1) (m^(-1)+ n^(-2))) – m^(-1\4m-1)/(m^(-2)+ n^(-2) ) = (5m^(-2)+ n^(-2)- 4m^(-2))/(4m^(-1) (m^(-2)+ n^(-2))) = (m^(-2)+ n^(-2))/(4m^(-1) (m^(-2)+ n^(-2))) = 1/(4m^(-1) ); 4) (b^(-1)+ 3c^(-1))/c^(-2) • bc/(b^(-2) c^(-1)+ 3b^(-1) c^(-2) ) = (b^(-1)+ 3c^(-1) )bc/(c^(-2) • b^(-1)•c^1 (b^(-1)+ 3c^(-1))) = b2c4.