Question

2x+3/x+2=x-1/x-2 cine mă ajuta

Answer 1

(2x+3)/(x+2)=(x-1)/(x-2)
(2x+3)(x-2)=(x+2)(x-1)
2x²+3x-4x-6=x²+2x-x-2
2x²-x-6=x²+x-2
x²-2x-4=0
x²-2x-4+5-5=0
x²-2x+1-5=0
(x-1)²-(√5)²=0
(x-1-√5)(x-1-√5)=0
(x-1-√5)=0   x=1+√5
(x-1+√5)=0  x=1-√5

sau
x²-2x-4=0
Δ=(-2)²-4×(-4)×1=4+16=20
x₁=[-(-2)+√20]/2=(2+2√5)/2=1+√5
x₂=[-(-2)-√20]/2=(2-2√5)/2=1-√5

Answer 2

Salut,

(2x+3)/(x+2) = (x-1)/(x-2)
(2x+3)(x-2) = (x-1)(x+2)
2x(x-2)+3(x-2) = x(x+2)-1(x+2)
2x²-4x+3x-6 = x²+2x-x-2
2x²-x-6 = x²+x-2
2x²-x-6-x²-x+2 = 0
x²-2x-4 = 0.

∆ = b²-4ac
∆ = 4+16
∆ = 20.

x1 = (-b-√∆)/2a
x1 = (2-2√5)/2
x1 = 2(1-√5)/2
x1 = 1-√5.

x2 = (-b+√∆)/2a
x2 = (2+2√5)/2
x2 = 2(1+√5)/2
x2 = 1+√5.

S = {1-√5 ; 1+√5}.



Succes! :3