(2х+1)^3(2х-3)^5=(2х+1)^5(2х-3)^3
(2х+1)^3(2х-3)^5-(2х+1)^5(2х-3)^3=0
(2х+1)^3(2х-3)^3((2х-3)^2-(2х+1)^2)=0
(2х+1)^3(2х-3)^3((2х-3)-(2х+1))((2х-3)+(2х+1))=0
(2х+1)^3(2х-3)^3(-4)(4x-2)=0
-8(2х+1)^3(2х-3)^3(2x-1)=0
Получаем:
(2х+1)^3=0 или (2х-3)^3=0 или 2x-1=0
(2х+1)^3=0
2х+1=0
x=-1/2
(2х-3)^3=0
2х-3=0
x=3/2
2x-1=0
x=1/2
Ответ: x=-1/2, x=3/2, x=1/2.
(2х+1)^3(2х-3)^5=(2х+1)^5(2х-3)^3
(2х+1)^3(2х-3)^5-(2х+1)^5(2х-3)^3=0
(2х+1)^3(2х-3)^3((2х-3)^2-(2х+1)^2)=0
(2х+1)^3(2х-3)^3((2х-3)-(2х+1))((2х-3)+(2х+1))=0
(2х+1)^3(2х-3)^3(-4)(4x-2)=0
-8(2х+1)^3(2х-3)^3(2x-1)=0
Получаем:
(2х+1)^3=0 или (2х-3)^3=0 или 2x-1=0
(2х+1)^3=0
2х+1=0
x=-1/2
(2х-3)^3=0
2х-3=0
x=3/2
2x-1=0
x=1/2
Ответ: x=-1/2, x=3/2, x=1/2.