Question

Rút gọn B

\(B=\dfrac{\sqrt{x}+1}{\sqrt{x}-2}+\dfrac{2\sqrt{x}}{\sqrt{x}+2}+\dfrac{5\sqrt{x}+2}{4-x}\)

Answer 1

\(B=\dfrac{\sqrt{x}+1}{\sqrt{x}-2}+\dfrac{2\sqrt{x}}{\sqrt{x}+2}+\dfrac{5\sqrt{x}+2}{4-x}(x \geq 0,x \neq 4)\)
`=(x+3\sqrtx+2+2x-4\sqrtx-5\sqrtx-2)/(x-4)`
`=(3x-6\sqrtx)/(x-4)`
`=(3\sqrtx(\sqrtx-2))/((\sqrtx-2)(\sqrtx+2))`
`=(3\sqrtx)/(\sqrtx+2)`

Answer 2

B = \(\dfrac{\sqrt{x}+1}{\sqrt{x}-2}+\dfrac{2\sqrt{x}}{\sqrt{x}+2}+\dfrac{5\sqrt{x}+2}{4-x}\) Đk: \(\left\{{}\begin{matrix}x\ge0\\x\ne4\end{matrix}\right.\)

    = \(\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)+2\sqrt{x}\left(\sqrt{x}-2\right)-5\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

    = \(\dfrac{x+3\sqrt{x}+2+2x-4\sqrt{x}-5\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

    = \(\dfrac{3x-6\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

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

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

Vậy B = \(\dfrac{3\sqrt{x}}{\sqrt{x}+2}\)  với \(\left\{{}\begin{matrix}x\ge0\\x\ne4\end{matrix}\right.\)