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Toán Lớp 9: Rút gọn: ( $\frac{1}{√x -1}$ – $\frac{1}{√x}$ ) : ( $\frac{√x +1}{√x -2}$ – $\frac{√x +2}{√x -1}$ )

Home/ Toán Lớp 9: Rút gọn: ( $\frac{1}{√x -1}$ – $\frac{1}{√x}$ ) : ( $\frac{√x +1}{√x -2}$ – $\frac{√x +2}{√x -1}$ )

Toán Lớp 9: Rút gọn: ( $\frac{1}{√x -1}$ – $\frac{1}{√x}$ ) : ( $\frac{√x +1}{√x -2}$ – $\frac{√x +2}{√x -1}$ )

Thanh Thu Tháng Chín 18, 2022 Toán học 1 Comment 0 views

Toán Lớp 9: Rút gọn:
( $\frac{1}{√x -1}$ – $\frac{1}{√x}$ ) : ( $\frac{√x +1}{√x -2}$ – $\frac{√x +2}{√x -1}$ )

Comments ( 1 )

hauthanhyen98
18 Tháng Chín, 2022 at 8:04 sáng

Reply

Giải đáp:

$\begin{array}{l}\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{1}{\sqrt{x}}\right):\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-2}-\dfrac{\sqrt{x}+2}{\sqrt{x}-1}\right)\\=\dfrac{\sqrt{x}-\sqrt{x}+1}{\sqrt{x}(\sqrt{x}-1)}:\dfrac{(\sqrt{x}-1)(\sqrt{x}+1)-(\sqrt{x}-2)(\sqrt{x}+2)}{(\sqrt{x}-2)(\sqrt{x}-1)}\\=\dfrac{1}{\sqrt{x}(\sqrt{x}-1)}:\dfrac{x-1-x+4}{(\sqrt{x}-2)(\sqrt{x}-1)}\\=\dfrac{1}{\sqrt{x}(\sqrt{x}-1)}:\dfrac{3}{(\sqrt{x}-2)(\sqrt{x}-1)}\\=\dfrac{1}{\sqrt{x}(\sqrt{x}-1)}\times\dfrac{(\sqrt{x}-2)(\sqrt{x}-1)}{3}\\=\dfrac{1}{\sqrt{x}}\times\dfrac{\sqrt{x}-2}{3}\\=\dfrac{\sqrt{x}-2}{3\sqrt{x}}\end{array}$

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