Lời giải:
ĐKXĐ: $x>-1$
PT $\Leftrightarrow (\sqrt{x+1}-\sqrt{x+2})+\frac{\sqrt{x+2}-\sqrt{x+1})}{\sqrt{x+1}}=0$
$\Leftrightarrow (\sqrt{x+1}-\sqrt{x+2})\left[1-\frac{1}{\sqrt{x+1}}\right]=0$
Dễ thấy $\sqrt{x+1}\neq \sqrt{x+2}$ nên $\sqrt{x+1}-\sqrt{x+2}\neq 0$
$\Rightarrow 1-\frac{1}{\sqrt{x+1}}=0$
\Leftrightarrow x=0$ (thỏa mãn)
Vậy.....
Cho biểu thức A=\(\left(\frac{x+2\sqrt{x}+4}{x\sqrt{x}-8}+\frac{x+2\sqrt{x}+1}{x-1}\right):\left(3+\frac{1}{\sqrt{x}-2}+\frac{2}{\sqrt{x}+1}\right)\)
Rút gọn A?
b, Tính A biết x=\(\frac{\sqrt{7+\sqrt{5}}+\sqrt{7-\sqrt{5}}}{\sqrt{7+2\sqrt{11}}}+\sqrt{83-18\sqrt{2}}\)
RG
A = \(\left(\frac{1}{x-\sqrt{x}}+\frac{1}{\sqrt{x}-1}\right):\frac{\sqrt{x}+1}{x-2\sqrt{x}+1}\)
B = \(\left(\frac{\sqrt{x}-2}{x-1}-\frac{\sqrt{x}+2}{x+2\sqrt{x}+1}\right).\left(\frac{1-x}{\sqrt{2}}\right)^2\)
Tính
3) \(\frac{\sqrt{x}-1}{\sqrt{x}+1}+\frac{2x-\sqrt{x}-1}{x-\sqrt{x}+1}-\frac{3x\sqrt{x}-2x+\sqrt{x}-3}{x\sqrt{x}+1}\)
4) \(\frac{15\sqrt{x}-11}{x+2\sqrt{x}-3}-\frac{3\sqrt{x}-2}{\sqrt{x}-1}-\frac{2\sqrt{x}+3}{\sqrt{x}+3}\)
5)\(\frac{\sqrt{x}-1}{\sqrt{x}-3}-\frac{\sqrt{x}+3}{\sqrt{x}-2}-\frac{x+5}{x-5\sqrt{x}+6}\)
Help !!! Mk đang cần gấp ,thank các ben
\(\left(\frac{1}{\sqrt{x}-\sqrt{x-1}}-\frac{x-3}{\sqrt{x-1}-\sqrt{2}}\right)\left(\frac{2}{\sqrt{2}-\sqrt{x}}-\frac{\sqrt{x}+\sqrt{2}}{\sqrt{2x}-x}\right)\)
a. A=(\(\frac{3x+16\sqrt{x}-7}{x+2\sqrt{x}-3}-\frac{\sqrt{x}+1}{\sqrt{x}+3}-\frac{\sqrt{x}+7}{\sqrt{x}-1}\)) : (\(2-\frac{\sqrt{x}}{\sqrt{x}-1}\))
b. B=(\(\frac{\sqrt{x}+1}{\sqrt{xy}+1}+\frac{\sqrt{xy}+\sqrt{x}}{1-\sqrt{xy}}+1\)) :( 1-\(\frac{\sqrt{xy}+\sqrt{x}}{\sqrt{xy}-1}-\frac{\sqrt{x}+1}{\sqrt{xy}+1}\))
c. C=( \(\frac{\sqrt{x}-4x}{1+4x}-1\)):(\(\frac{1+2x}{1-4x}-\frac{2\sqrt{x}}{2\sqrt{x}}-1\))
d. D=(\(\frac{\sqrt{a-b}}{\sqrt{a+b}+\sqrt{a+b}}+\frac{a-b}{\sqrt{a^2-b^2}-a+b}\))\(\frac{a^2+b^2}{\sqrt{a^2-b^2}}\)
e. E=\(\frac{\left(\sqrt{a}-\sqrt{b}\right)+4\sqrt{ab}}{\sqrt{a}+\sqrt{b}}-\frac{a\sqrt{b}-b\sqrt{a}}{\sqrt{ab}}-b\)
Bài 1: Tính :
\(C=\sqrt{\frac{3\sqrt{3}-4}{2\sqrt{3}+1}}-\sqrt{\frac{\sqrt{3}+4}{5-2\sqrt{3}}}\)
\(B=\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+....+\frac{1}{\sqrt{99}+\sqrt{100}}\)
\(D=\sqrt{1+\sqrt{3+\sqrt{13+4\sqrt{3}}}}+\sqrt{1-\sqrt{3-\sqrt{13-4\sqrt{3}}}}\)
Bài 2 : Cho \(P=\left(\frac{1}{\sqrt{x}-1}+\frac{x-\sqrt{x}+6}{x+\sqrt{x}-2}\right):\left(\frac{\sqrt{x}+1}{\sqrt{x}+2}+\frac{x-\sqrt{x}-2}{x+\sqrt{x}+2}\right)\)
a, Rút gọn P
b, Tìm GTNN
c, Tìm x để \(P.\frac{x-1}{x^2+8x}< -2\)
Gpt: a) \(\sqrt[4]{3\left(x+5\right)}-\sqrt[4]{11-x}=\sqrt[4]{13+x}-\sqrt[4]{3\left(3-x\right)}\)
b) \(\frac{1+2\sqrt{x}-x\sqrt{x}}{3-x-\sqrt{2-x}}=2\left(\frac{1+x\sqrt{x}}{1+x}\right)\) c) \(\sqrt{x+1}+\frac{4\left(\sqrt{x+1}+\sqrt{x-2}\right)}{3\left(\sqrt{x-2}+1\right)^2}=3\)
d) \(\sqrt{\frac{x-2}{x+1}}+\frac{x+2}{\left(\sqrt{x+2}+\sqrt{x-2}\right)^2}=1\) e) \(2x+1+x\sqrt{x^2+2}+\left(x+1\right)\sqrt{x^2+2x+2}=0\)
f) \(\sqrt{2x+3}\cdot\sqrt[3]{x+5}=x^2+x-6\)
\(P=\frac{x\sqrt{x}-1}{x-\sqrt{x}}-\frac{x\sqrt{x}+1}{x+\sqrt{x}}+\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)\left(\frac{\sqrt{x}+1}{\sqrt{x-1}}+\frac{\sqrt{x}-1}{\sqrt{x}+1}\right)-2\sqrt{x}\)
rút gọn P
1. Rút gọn
P=\(2\sqrt{1+\frac{1}{4}\left(\sqrt{\frac{1}{x}}-\sqrt{x}\right)^2}:\left[\sqrt{1+\frac{1}{4}\left(\sqrt{\frac{1}{x}}-\sqrt{x}\right)^2}-\frac{1}{2}\left(\sqrt{\frac{1}{x}}-\sqrt{x}\right)^2\right]\)
