Question

x+2 supra x-1 - x+5 supra x+1=3.   Cat e x-ul?        

Answer 1

(x+2)/(x-1) - (x+5)/(x+1)=3  aducem la acelasi numitor

(x+2)(x+1)- (x+5)(x-1)= 3(x+1)(x-1)

x²+x+2x+2- (x²-x+5x-5)=3(x²-1)

x² +3x +2 -x²+x-5x +5= 3x²-3

4x-5x+7=3x²-3

-x+7=3x²-3

3x²-x+7+3=0

3x²-x+10=0

a=3
b=-1
c=10
Δ= 1-3*10*4= 1- 120 =-119 ⇒S{Ф}   Δnu are solutii cand are valoare negativa

Answer 2

$\frac{x+2}{x-1}-\frac{x+5}{x+1} =3$

aducem la acelasi numitor comun
$[tex](x+1)(x+2)-(x-1)(x+5)=3 x^{2}-3 \\ \\ x^{2} +2x+x+2- x^{2} -5x+x+5- 3x^{2} +3=0 \\ \\ -3 x^{2} -x+10=0 \\ \\ a=-3 \\ b=-1 \\ c=10 \\ \\ Δ=b ^{2}-4ac \\ ]Δ=(-1) ^{2} -4(-3*10) \\ \\ Δ=121 \\ \\ x_{1,2} = \frac{-b+-\sqrt{Δ} }{2a}$[/tex][tex] x_{1,2}= \frac{-1+-11}{-6} \\ \\ x_{1} = \frac{-1-11}{-6} \\ \\ x_{1}=2 \\ \\ x_{2} = \frac{-1+11}{-6} \\ \\ x_{2}= \frac{10}{-6} \\ \\ x_{2} = \frac{5}{-3} } [/tex]