Toán Lớp 9: Rút gọn BT sau :
B= $\frac{căn x }{x-1}$ + $\frac{2}{2- căn x}$ + $\frac{1}{căn x+2}$
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Toán Lớp 9: Rút gọn BT sau :
B= $\frac{căn x }{x-1}$ + $\frac{2}{2- căn x}$ + $\frac{1}{căn x+2}$
Comments ( 2 )
Giải đáp+Lời giải và giải thích chi tiết:
B = {\sqrt{x}}/{x-1} + 2/{2 -\sqrt{x}} + 1/{\sqrt{x} +2} (ĐK: x \ne 1; x \ge 0)
B = {\sqrt{x}(\sqrt{x} -2)(\sqrt{x} +2)}/{(x-1)(\sqrt{x} +2)(\sqrt{x} -2)} – {2(x-1)(\sqrt{x} +2)}/{(\sqrt{x} -2)(x-1)(\sqrt{x} +2)} + {(x-1)(\sqrt{x} -2)}/{(x-1)(\sqrt{x}-2)(\sqrt{x} +2)}
B = {\sqrt{x}(x-4) – (2x-2)(\sqrt{x} +2) + x\sqrt{x} -2x -\sqrt{x} +2}/{(x-1)(x-4)}
B ={x\sqrt{x} -4\sqrt{x} -2x\sqrt{x} -4x +2\sqrt{x} +4+x\sqrt{x} -2x -\sqrt{x} +2}/{(x-1)(x-4)}
B = {-3\sqrt{x} -6x +6}/{(x-1)(x-4)}
B=(sqrt{x})/(x-1)+2/(2-sqrt{x})+1/(sqrt{x}+2)
=(sqrt{x})/(x-1)+(2(2+sqrt{x}))/(4-x)+(2-sqrt{x})/(4-x)
=(sqrt{x})/(x-1)+(4+2sqrt{x}+2-sqrt{x})/(4-x)
=(sqrt{x})/(x-1)+(6-sqrt{x})/(4-x)
=(sqrt{x}(4-x))/((x-1)(4-x))+((6+sqrt{x})(x-1))/((x-1)(4-x))
=(4sqrt{x}-xsqrt{x}+6x-6+xsqrt{x}-sqrt{x})/((x-1)(4-x))
=(6x+3sqrt{x}-6)/((x-1)(4-x)).