Question

Bài 1:Tìm tất cả các số nguyên x để các phân số sau có giá trị là số nguyên

a,\(A=\frac{x+1}{x-2}\left(x\ne2\right)\)

b,\(B=\frac{2x-1}{x+5}\left(x\ne-5\right)\)

Answer 1

a, Để phân số đạt giá trị nguyễn 

\(\Rightarrow x+1⋮x-2\)

\(\Rightarrow x-2+3⋮x-2\)

mà \(x-2⋮x-2\Rightarrow3⋮x-2\)

\(\Rightarrow x-2\inƯ\left(3\right)=\left\{\pm1;\pm3\right\}\)

\(\Rightarrow x\in\left\{3;5\pm1\right\}\)

Answer 2

b,Tương tự :

\(2x-1⋮x+5\)

\(\Rightarrow2x+10-11⋮x+5\)

\(2\left(x+5\right)-11⋮x+5\)

mà \(2\left(x+5\right)⋮x+5\Rightarrow11⋮x+5\)

\(\Rightarrow x+5\inƯ\left(11\right)=\left\{\pm1;\pm11\right\}\)

\(x\in\left\{-4;\pm6;-16\right\}\)

Answer 3

a, Để \(A\in Z\)\(\Leftrightarrow x+1⋮x-2\)\

Ta có:              \(\hept{\begin{cases}x-2⋮x-2\\x+1⋮x-2^{ }_{ }\end{cases}}\) \(\Rightarrow\) \(x-2-\left(x+1\right)⋮x-2\)

\(\Rightarrow-3⋮x-2\)mà \(x\in Z\Rightarrow x-2\in Z\Rightarrow x-2\inƯ\left(-3\right)\)\(\in\left(1;-1,3;-3\right)\)

\(x\in\left(3;1;5;-1\right)\)Vậy: \(x\in\left(1;3;5;-1\right)\)thì \(A\in Z\)

Answer 4

b, Để \(B\in Z\Leftrightarrow2x-1⋮x+5\)

Mà    \(\hept{\begin{cases}x+5⋮x+5\\2x-1⋮x+5\end{cases}}\)\(\Rightarrow\)\(2x+10-\left(2x-1\right)⋮x+5\)\(\Rightarrow11⋮x+5\)

Vì \(x\in Z\Rightarrow x+5\in Z\Rightarrow x+5\inƯ\left(11\right)\)\(\in\left(1;11;-1;-11\right)\)

                       \(\Rightarrow x\in\left(-4;6;-6;-16\right)\)

Vậy : ...........