2x+3 x-1 2(2x+3) 5(x-1) 10(3x)
1) ........... - ........ = 3x donc : .............. - ........... = .............
5 2 10 10 10
(4x+6) -(5x-5) 30x
........................ =. .........
10 10
4x+6-5x+5 = 30x
-x+11 =30x
-x-30x=-11
-31x= -11
x=-11/-31 ; x= 11/31 ; S={11/31}
3) (x+2)² = (2x-3)² ;;;; (x+2)²-(2x-3)²=0 ;;;;[(x+2)+(2x-3)][(x+2)-(2x-3)]=0
(x+2+2x-3)(x+2-2x+3)=0
(3x-1)(-x+5)=0
donc : 3x-1=0 ;;;3x=1 ,,, x=1/3,
ou :-x+5=0 ;; -x = -5 ,,, x= -5/-1=5 ; S={1/3 ; 5}
5) 11x²-5x=0 ;;;; x(11x-5)=0 ...x=0 ou 11x-5=0 , 11x=5 ;. x=5/11
S={0 ; 5/11}
7) 5x²+4=0 ;;;.5x²= -4 ;;; x² = -4/5 pas de solutions, parce que x² est
toujours positif , -4/5 est négatif
2x-1 x x²+1 (2x-1)(x+3) x(x-3) x²+1
12) ........ - ........... =........... →,, ................. - ................ = ..........
x-3 x+3 x²-9 (x-3)(x+3) (x+3)(x-3) x²-9
2x²+6x-x-3 x²-3x x²+1
................... - .......... = ........
x²-9 x²-9 x²-9
2x²+5x-3-x²+3x x²+1
.......................... = ............
x²-9 x²-9
x²+8x-3 =x²+1
x²+8x-x²=1+3 ( x²-x²=0)
8x=4
x=4/8 ;x= 1/2 ;.S ={1/2}
