Question

wszystko załączam w załączniku.

Licze na pomoc .

Answer 1

a)

(x²-1)/(x+1)²

(x+1)²≠0

x≠-1

D=R\{-1}

 

(x²-1)/(x+1)² =

(x-1)(x+1)/(x+1)²=

(x-1)/(x+1)

 

b)
(x²-4)/(x²-4x+4)

x²-4x+4≠0

x²-4x+4=

x²-2x-2x+4=

x(x-2)-2(x-2)=

(x-2)(x-2)=

(x-2)²

x≠2

D=R\{-2}

 

(x²-4)/(x²-4x+4)=

(x-2)(x+2)/(x-2)²=

(x+2)/(x-2)

 

(-1+2)/(-1-2)=

1/(-3)=

-1/3

 

c)

(-x²+x⁶)/(x⁴-2x³+x²)

(x⁴-2x³+x²)≠0

x⁴-2x³+x²=

x²(x²-2x+1)=

x²(x²-x-x+1)=

x²(x(x-1)-1(x-1))=

x²(x-1)(x-1)=

x²(x-1)²

x≠0 ∨ x≠1

D=R\{0,1}

 

(-x²+x⁶)/(x⁴-2x³+x²)=

x²(x⁴-1)/x²(x-1)²=

(x²-1)(x²+1)/(x-1)²=

(x-1)(x+1)(x²+1)/(x-1)²=

(x²+1)(x+1)/(x-1)

 

((-1)²+1)(-1+1)/(-1-1)=

(2*0)/-2=0

 

d)

(2x²+12x+18)/(x²+5x+6)

x²+5x+6≠0

Δ=5²-4*1*6

Δ=25-24

Δ=1

√Δ=1

 

x₁=(-5-1)/(2*1)

x₁=-6/2

x₁=-3

 

x₂=(-5+1)/(2*1)
x₂=-4/2

x₂=-2

 

x²+5x+6=(x+3)(x+2)

x≠-3 ∨ x≠-2

D=R\{-2,-3}

 

(2x²+12x+18)/(x²+5x+6)=

(x²+6x+9)/(x+3)(x+2)=

(x+3)²/(x+3)(x+2)=

(x+3)/(x+2)

 

(-1+3)/(-1+2)=

2/1=

2