Question

Cho A=\(\left(\dfrac{2x+1}{\sqrt{x^3}-1}-\dfrac{1}{\sqrt{x}-1}\right):\left(1-\dfrac{x+4}{x+\sqrt{x}+1}\right)\)

a)Rút gọn A

b)Tìm x tự nhiên để A có giá trị nguyên dương

Answer 1

a: \(=\dfrac{2x+1-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}:\dfrac{x+\sqrt{x}+1-x-4}{x+\sqrt{x}+1}\)

\(=\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\cdot\dfrac{1}{\sqrt{x}-3}=\dfrac{\sqrt{x}}{\sqrt{x}-3}\)

b: Để A là số nguyên dương thì

\(\left\{{}\begin{matrix}\sqrt{x}-3+3⋮\sqrt{x}-3\\\sqrt{x}-3>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>9\\\sqrt{x}-3\in\left\{1;-1;3;-3\right\}\end{matrix}\right.\)

=>\(x\in\left\{16;36\right\}\)