A=\(\frac{x\sqrt{x}-2x-49}{x+3\sqrt{x}-4}-\frac{\sqrt{x}-4}{\sqrt{x}+4}-\frac{2\sqrt{x}+8}{\sqrt{x}-1}\)
Rút gọn A
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=\(\frac{x\sqrt{x}-2x+28}{x-3\sqrt{x}-4}\)- \(\frac{\sqrt{x}-4}{\sqrt{x}+1}\)- \(\frac{\sqrt{x}+8}{\sqrt{x}-4}\)
= \(\frac{x\sqrt{x}-2x+28-\left(x-16\right)-\left(\sqrt{x}+1\right)\left(\sqrt{x}+8\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)
=\(\frac{x\sqrt{x}-2x+28-x+16-\left(x+9\sqrt{x}+8\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)
=\(\frac{x\sqrt{x}-3x+44-x-9\sqrt{x}-8}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)
=\(\frac{x\sqrt{x}-9\sqrt{x}-4x+36}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)
=\(\frac{\sqrt{x}\left(x-9\right)-4\left(x-9\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)= \(\frac{\left(\sqrt{x}-4\right)\left(x-9\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)
=\(\frac{x-9}{\sqrt{x}+1}\)
a) \(\sqrt{7-4\sqrt{3}}-\sqrt{7+4\sqrt{3}}\)
\(=\sqrt{4-4\sqrt{3}+3}-\sqrt{4+4\sqrt{3}+3}\)
\(=\sqrt{\left(2-\sqrt{3}\right)^2}-\sqrt{\left(2+\sqrt{3}\right)^2}\)
\(=\left|2-\sqrt{3}\right|-\left|2+\sqrt{3}\right|\)
\(=2-\sqrt{3}-2-\sqrt{3}\)
\(=-2\sqrt{3}\)