Question

tìm x để (x+3)/(1-x) lá số nguyên

 

Answer 1

Ta có:\(\dfrac{x+3}{1-x}=\dfrac{-\left(1-x\right)+4}{1-x}=-1+\dfrac{4}{1-x}\)

Để \(\dfrac{4}{1-x}\) nguyên thì 1-x∈Ư₍₄₎={1;-1;2;-2;4;-4}

                             ⇔ x={0;2;-1;3;-3;5}

Answer 2

Để \(\dfrac{x+3}{1-x}\) là số nguyên thì \(x+3⋮x-1\)

\(\Leftrightarrow x-1\in\left\{1;-1;2;-2;4;-4\right\}\)

hay \(x\in\left\{2;0;3;-1;5;-3\right\}\)