Question

cho biểu thức T=\(\dfrac{x+6\sqrt{x}+9}{\sqrt{x}+3}-\dfrac{x-4}{\sqrt{x}-2}\)tìm x để T có nghĩa và rút gọn T

Answer 1

ĐKXĐ: \(\left\{{}\begin{matrix}x\ge0\\x\ne4\end{matrix}\right.\)

Ta có: \(T=\dfrac{x+6\sqrt{x}+9}{\sqrt{x}+3}-\dfrac{x-4}{\sqrt{x}-2}\)

\(=\sqrt{x}+3-\sqrt{x}-2\)

=1

Answer 2

Để T có nghĩa 

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\\sqrt{x}+3\ne0\\\sqrt{x}-2\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x\ne4\end{matrix}\right.\)

\(T=\dfrac{x+6\sqrt{x}+9}{\sqrt{x}+3}-\dfrac{x-4}{\sqrt{x}-2}=\dfrac{\left(\sqrt{x}+3\right)^2}{\sqrt{x}+3}-\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\sqrt{x}-2}=\sqrt{x}+3-\left(\sqrt{x}+2\right)=1\)