Răspuns:
[tex]E(x)=(\frac{1}{x+2}+\frac{3}{x-2}+\frac{x}{4-x^2})*(x-2)[/tex]
a) x+2≠0 => x≠-2
x-2≠0 =>x≠2
[tex]4-x^2=0 => (2-x)(2+x)=0\\2-x=0 \\x=2\\2+x=0\\x=-2[/tex](aici nu a mers sa pun semnul de diferit)
x∈R\{-2,2}
b)
amplificam sa aducem la acelasi numitor si inmultesc cu -1 primele 2
[tex]E(x)=(\frac{1}{x+2}+\frac{3}{x-2}+\frac{x}{4-x^2})*(x-2)=(\frac{2-x}{(2+x)(2-x)}-\frac{3(2+x)}{(2+x)(2-x)}+\frac{x}{(2-x)(2+x)})*-(2-x)=-(\frac{2-x-6-3x+x}{(2-x)(2+x)})*(2-x)=-(\frac{-4-3x}{2+x})=\frac{3x+4}{2+x}[/tex]
c)
3x+4|2+x
3x+4|3x+4
6x+8|4x+6
6x+8=4x+6
2x=-2
x=-1
iar daca luam x=0 rezulta
[tex]\frac{3x+4}{2+x}=\frac{4}{2}=2[/tex]
Explicație pas cu pas:
