Rút gọn các biểu thức...
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Rút gọn các biểu thức sau:
\(A=\left(\dfrac{1}{\sqrt{x}-3}+\dfrac{1}{\sqrt{x}+3}\right)\left(1-\dfrac{3}{\sqrt{x}}\right)\)
\(B=\left(\dfrac{\sqrt{x}}{\sqrt{x}-2}+\dfrac{1}{\sqrt{x}+2}+\dfrac{6-7\sqrt{x}}{x-4}\right)\left(\sqrt{x}+2\right)\)
\(C=\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{\sqrt{a}}{a-\sqrt{1}}\right):\dfrac{\sqrt{a}+1}{a-1}\)
\(D=\left(\dfrac{x-2}{x+2\sqrt{x}}+\dfrac{1}{\sqrt{x}+2}\right).\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\)\(E=\left(1+\dfrac{x+\sqrt{x}}{\sqrt{x}+1}\right)\left(1+\dfrac{x-\sqrt{x}}{1-\sqrt{x}}\right)\)
A = \(\left(\frac{1}{\sqrt{x}-3}+\frac{1}{\sqrt{x}+3}\right).\left(1-\frac{3}{\sqrt{x}}\right)\)
\(A=\left(\frac{\sqrt{x}+3+\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\right)\left(\frac{\sqrt{x}-3}{\sqrt{x}}\right)\)
\(A=\frac{2\sqrt{x}}{\sqrt{x}+3}.\frac{1}{\sqrt{x}}\)
\(A=\frac{2}{\sqrt{x}+3}.1=\frac{2}{\sqrt{x}+3}\)
\(B=\left(\frac{\sqrt{x}}{\sqrt{x}-2}+\frac{1}{\sqrt{x}+2}+\frac{6-7\sqrt{x}}{x-4}\right)\left(\sqrt{x}-2\right)\) \(ĐKXĐ:x\ne4;x\ge0\)
\(B=\left(\frac{\sqrt{x}.\left(\sqrt{x}+2\right)+1.\left(\sqrt{x}-2\right)+6-7\sqrt{x}}{\left(\sqrt{x}-2\right).\left(\sqrt{x}+2\right)}\right).\left(\sqrt{x}+2\right)\)
\(B=\frac{x+2\sqrt{x}+\sqrt{x}-2+6-7\sqrt{x}}{\sqrt{x}-2}\)
\(B=\frac{x-4\sqrt{x}+4}{\sqrt{x}-2}\)
\(B=\frac{\left(\sqrt{x}\right)^2-2.2.\sqrt{x}+2^2}{\sqrt{x}-2}\)
\(B=\frac{\left(\sqrt{x}-2\right)^2}{\sqrt{x}-2}\)
\(B=\sqrt{x}-2\)
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