Question

tìm x ϵ Z để (x+4/x-2)+(2x-5/x-2)

Answer 1

\(\dfrac{x+4}{x-2}+\dfrac{2x-5}{x-2}=\dfrac{3x-1}{x-2}\)

Answer 2

Giải:

\(\left(\dfrac{x+4}{x-2}\right)+\left(\dfrac{2x-5}{x-2}\right)\) 

=\(\dfrac{x+4+2x-5}{x-2}\) 

=\(\dfrac{x.\left(1+2\right)+4-5}{x-2}\) 

=\(\dfrac{x.3-1}{x-2}\) 

⇒3x-1 ⋮ x-2

⇒3x-6+5 ⋮ x-2

⇒5 ⋮ x-2

⇒x-2 ∈ Ư(5)={-5;-1;1;5}

Ta có bảng:

x-2=-5 ➜x=-3

x-2=-1 ➜x=1

x-2=1 ➜x=3

x-2=5 ➜x=7

Vậy x ∈ {-3;1;3;7}

Chúc bạn học tốt!