Question

Rút gọn biểu thức sau:

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

Answer 1

ĐKXĐ:\(x>0;x\ne4\)

B=\(\left(\dfrac{1}{x-4}-\dfrac{1}{x-4\sqrt{x}+4}\right)\cdot\dfrac{x+2\sqrt{x}}{\sqrt{x}}=\dfrac{\sqrt{x}-2-\sqrt{x}-2}{\left(\sqrt{x}-2\right)^2\left(\sqrt{x}+2\right)}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)}{\sqrt{x}}=\dfrac{-4}{\left(\sqrt{x}-2\right)^2\left(\sqrt{x}+2\right)}\cdot\left(\sqrt{x}+2\right)=-\dfrac{4}{\left(\sqrt{x}-2\right)^2}\)

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