РОЗДІЛ 2. Раціональні вирази - Вправи 50 - 200 » 163

163. Спростіть вираз: 1) 〖3x-1〗^(\3)/2 + (x-2)/6 – 〖2x-3〗^(\2)/3 = (9x-3+x-2-4x+6)/6 = (6x+1)/6; 2) 〖2a-3b〗^(\a)/〖5ab〗^2 – 〖2b-3a〗^(\b)/(〖5a〗^2 b) = (a(2a-3b)( -b(2b-3a))/(〖5a〗^2 b^2 ) = (〖2a〗^2- 3ab- 〖2b〗^2+ 3ab)/(〖5a〗^2 b^2 ) = (〖2a〗^2- 〖2b〗^2)/(〖5a〗^2 b^2 ); 3) (x-y)/〖2xy-3y〗^2 – (y-x)/〖3xy-2x〗^2 = (x-y)/(y(2x-3y)) – (y-x)/(x(3y-2x)) = 〖x-y〗^(\x)/(y(2x-3y)) + 〖y-x〗^(\y)/(x(2x-3y)) = (x^2- xy+ y^2- xy)/(xy(2x-3y)) = (x^2- 2xy+ y^2)/(xy(2x-3y)) = 〖(x-y)〗^2/(xy(2x-3y)); 4) 〖3y-x〗^(\5)/(〖21x〗^2 y^2 ) – 〖5x-y〗^(\3)/(〖35x〗^3 y) = (15y-5x-15x+3y)/(〖105x〗^3 y^2 ) = (-20x+18y)/(〖105x〗^3 y^2 ).