Question

Решите дробное рациональное уравнение: 72/x-72/x+4 =3

Answer 1

72/х - 72/(х+4) = 3
(72(х+4))/(х(х+4)) - 72х / х(х+4) = 3
(72(х+4) - 72х)/(х(х+4)) = 3
(72х + 288 - 72х)/(х(х+4)) = 3

288 / (х^2 + 4х) = 3
х^2 + 4х = 96
х^2 + 4х - 96 = 0
(х-8)*(х+12) = 0
х1 = 8 ; х2 = -12

Ответ: 8 ; -12