Question

Answer 1

a) Để \(\dfrac{5}{x-1}\) là số nguyên thì \(5⋮x-1\)

\(\Leftrightarrow x-1\inƯ\left(5\right)\)

\(\Leftrightarrow x-1\in\left\{1;-1;5;-5\right\}\)

\(\Leftrightarrow x\in\left\{2;0;6;-4\right\}\)

b) Để \(\dfrac{2x+5}{x+1}\) là số nguyên thì \(2x+5⋮x+1\)

\(\Leftrightarrow3⋮x+1\)

\(\Leftrightarrow x+1\in\left\{1;-1;3;-3\right\}\)

hay \(x\in\left\{0;-2;2;-4\right\}\)