Question

Va rog sa ma ajutati!
1. Se da expresia E(x) = ($\frac{2}{x=5}$ - $\frac{x-6}{x²-25}$ + $\frac{x}{x-5}$) : $\frac{2x²+x-6}{25-x²}$.
a. Aratati ca (x+2)(2x-3)= 2x²+x-6

Answer 1

a)2x²+x-6=0
Δ=1+48=49
x1=6/4=3/2
x2=-8/4=-2
2x²+x-6=(x+2)(x-3/2)=(x+2)(3x-2)

1)
E(x)={[2(x+5)-(x-6)+x(x+5)]/(x²-25)}:[(x+2)(2x-3)]/(-)(x²-25)
E(x)=[(2x+10-x+6+x²+5x)/(x²-25)]·(-1)(x²-25)/[(x+2)(2x-3)] simplificam cu x²-25
E(x)=(-1)(x²+6x+16)/[(x+2)(2x-3)]
cond.x≠{-2,3/2}
x²+6x+16=0
Δ=36-64=-28
Δ<0