Вправа 301 - 400 » 332

332. Спростіть вираз. a) ((2x-1)/(x+1) – x)( 3/(x^2+1) – 1/(x+1) – 3/(x^2- x+1)) = (2x-1-x^2- x )/(x+1) • (3-x^2+ x-1-3x-3 )/(x^3+1) = (〖-(x〗^2- x+1))/(x+1) • 〖-(x+1)〗^2/(x^3+1) = (x+1)/(x+1) = 1; б) 〖3x〗^2/(a^2- x^2 ) – 3a • (1/(a- x) – x/(a^3- x^3 ) • (a^2+ ax+x^2 )/(a+ x)) = –3; 1. x/((a- x) 〖(a〗^2+ ax+x^2) ) • (a^2+ ax+x^2 )/(a+ x) = x/(a^2-x^2 ); 2. 1/(a- x) – x/(a^2-x^2 ) = (a+ x- x)/(a^2-x^2 ) = a/(a^2-x^2 ); 3. 3a • a/(a^2-x^2 ) = 〖3a〗^2/(a^2-x^2 ); 4. 〖3x〗^2/(a^2-x^2 ) – 〖3a〗^2/(a^2-x^2 ) = (〖3(x〗^2-a^2) )/(a^2- x^2 ) = –3;