1.2x/2x-3=x+2/x+1⇒x(x+1)=(x+2)(2x-3)⇒x²+x=2x²-3x+4x-6⇒x²-2x²+x+3x-4x+6=0⇒
-x²+6=0⇒-x²=-6 inmultim cu -1⇒x²=6⇒x indice 1=plus radical din 6 si x indice 2=minus radical din 6
ex 2.3x-1/x+2=3x/x-1⇒(3x-1)(x-1)=3x(x+2)⇒3x²-3x-x+1=6x²+6x⇒3x²-6x²-3x-x-6x+1=0⇒-3x²-10x+1=0 inmultim cu -1⇒3x²+10x-1=0⇒calculam Δ=b²-4ac⇒Δ=100+12=112⇒x indice 1=(-10+√112)/6=(-10+√2²·2²·7)6=(-10+2²√7)6=2(-5+2√7)/6 simplificam cu 2⇒x indice 1=(-5+2√7)/3
x indece 2=(-10-√112)6=...........facem calculele c mai sus⇒x indice 2=(-5-2√7)/3
ex.3.....7x-3/x+5=7x-5/x+2⇒(7x-3)(x+2)=(x+5)(7x-5)⇒7x²+14x-3x-6=7x²-5x+35x-25⇒
7x²-7x²+14x-3x+5x-35x=-6-25⇒-19x=-19 inmultim cu -1⇒19x=19⇒x=19/19⇒x=1
ex.4 ....x+1/x+2=x+2/x+1⇒(x-1)(x+1)=(x+2)(x+2)⇒x²+x-x-1=x²+2x+2x+4⇒
x²-1=x²+4x+4⇒x²-x²-4x=4+1⇒-4x=5 inmultim cu -1⇒4x=-5⇒x=-5/4
ex.5....(x-√2)/x=x/(x+√2)⇒(x-√2)(x+√2)=x·x⇔desfacem parantezele
x²+√2·x-√2·x-√4=x²⇒x²-x²-2=0⇒0-2=0 nu are solutie
ex.6....(0,3x-1)/5x=0,3/5x⇒(0,3x-1)·5x=0,3·5x⇒1,5x²-5x=1,5x⇒1,5x²-5x-1,5x=0⇒
1,5x²-6,5x=0⇒x(1,5x-6,5)=0⇒x indice1=0 si 1,5x-6,5=0⇒1,5x=6,5⇒x=6,5/1,5⇒
x indice 2=4, (3)
ex.7.....(2x-1)/(6x-3)=-1/6⇒(-6)(2x-1)=(-1)(6x-3)⇒-12x+6=-6x+3⇒-12x+6x=3-6⇒-6x=-3 inmultim cu -1⇒6x=3⇒x=3/6 simplificam⇒x=1/3
ex.8....(3x-1)/6x-2=4x-1/8x-2⇒(3x-1)(8x-2)=(4x-1)(6x-2)⇒24x²-6x-8x+2=24x²-8x-6x+2⇒24x²-14x+2=24x²-14x+2⇒24x²-24x²-14x+14x=2-2⇒0=0 nu are solutii
succes maine, cred ca as merita un punctaj mai mare ca au fost 8 ex. si mi-a luat ceva timp sa le rezolv
incearca sa te uiti la modele si sa faci multe exercitii, numai asa poti invata
