Question

Wykonaj działania i podaj konieczne założenia:

Answer 1

a)

D:

x-3≠0 ∧ x≠0

x≠3 ∧ x≠0

x∈R\{0;3}

3/(x-3)+(4+x)/x=3x/x(x-3)+(x-3)(4+x)/x(x-3)=[3x+x²+x-12]/x(x-3)=

(x²+4x-12)/(x²-3x)

b)

x-3≠0 ∧ x+3≠0

x≠3 ∧ x≠-3

x∈R\{-3;3}

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

[(x²+x-6)-(x²-4x+3)]/(x²-9)=[x²+x-6-x²+4x-3]/(x²-9)=(5x-9)/(x²-9)

c)

x²-9≠0

(x-3)(x+3)≠0

x≠3 ∧ x≠-3

x∈R\{-3;3}

[(x+3)/2]*[16/(x²-9)]=[(x+3)/2]*[16/(x-3)(x+3)]=8/(x-3)

d)

x+6≠0 ∧ 2x+12≠0 ∧ 3/(2x+12)≠0

x≠-6 ∧ x≠-6 ∧ x∈R

x∈R\{-6}

[1/(x+6)]/[3/(2x+12)]=[1/(x+6)]*[2(x+6)/3]=2/3