Вправи 201 - 300 » 204

204. Спростіть вираз: 1) (〖2x〗^(\1+3y)/(1-3y) + 〖2x〗^(\1-3y)/(3y+1)) • (〖9y〗^2+ 1-6y)/4x = (2x+6xy+2x-6xy)/((1-3y)(1+3y)) • (〖9y〗^2- 6y+1)/4x = (4x • 〖(9y〗^2- 6y+1))/((1-3y)(1+3y)•4x) = 〖(3y-1)〗^2/((1-3y)(1+3y)) = 〖(1-3y)〗^2/((1-3y)(1+3y)) = (1-3y)/(1+3y); 2) ((y^2- x^2)/(m^2- n^2 ) • (m+n)/(x-y) – x/(n-m)) • (m-n)/2y = ((〖(y〗^2- x^2) •(m+n))/(〖(m〗^2- m^2)(x-y)) + x/(m-n)) • (m-n)/2y = (((y-x)•(y+x)•(m+n))/((m-n)•(m+n)(x-y)) + x/(m-n)) • (m-n)/2y = (–((x-y)(x+y))/((m-n)(x-y)) + x/(m-n)) • (m-n)/2y = (-x-y+x)/(m-n) • (m-n)/2y = –y/(m-n) • (m-n)/2y = –(y •(m-n))/((m-n)•2y) = –0,5.