Question

P=(x/x^2-4+2/2-x+1/x+2):1/x+2

a, tìm đk và rút gọn biểu thức P

b, tìm x nguyên để P nguyên

Answer 1

a) ĐKXĐ: \(x\notin\left\{2;-2\right\}\)

Ta có: \(P=\left(\dfrac{x}{x^2-4}+\dfrac{2}{2-x}+\dfrac{1}{x+2}\right):\dfrac{1}{x+2}\)

\(=\dfrac{x-2\left(x+2\right)+x-2}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x+2}{1}\)

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

\(=\dfrac{2}{x-2}\)

Answer 2

b) Để P nguyên thì \(2⋮x-2\)

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

hay \(x\in\left\{3;1;4;0\right\}\)