Toán Lớp 9: Rút gọn
$\frac{\sqrt{x}}{\sqrt{x} -5}$ + $\frac{10\sqrt{x}}{25-x}$ – $\frac{5}{\sqrt{x}+5}$
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Toán Lớp 9: Rút gọn
$\frac{\sqrt{x}}{\sqrt{x} -5}$ + $\frac{10\sqrt{x}}{25-x}$ – $\frac{5}{\sqrt{x}+5}$
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ĐKXĐ: x>=0;xne25
=\frac{\sqrt{x}}{\sqrt{x}-5}-\frac{10\sqrt{x}}{x-25}-\frac{5}{\sqrt{x}+5}
=\frac{\sqrt{x}(\sqrt{x}+5)-10\sqrt{x}-5(\sqrt{x}-5)}{(\sqrt{x}+5)(\sqrt{x}-5)}
=\frac{x+5\sqrt{x}-10\sqrt{x}-5\sqrt{x}+25}{(\sqrt{x}+5)(\sqrt{x}-5)}
=\frac{x-10\sqrt{x}+25}{(\sqrt{x}+5)(\sqrt{x}-5)}
=\frac{(\sqrt{x}-5)^2}{(\sqrt{x}+5)(\sqrt{x}-5)}
=\frac{\sqrt{x}-5}{\sqrt{x}+5}