\(P=1:
\left(\frac{x+2}{x\sqrt{x}+1}+\frac{\sqrt{x}+1}{x+\sqrt{x}+1}-\frac{\sqrt{x}+1}{x-1}\right)\)
Rút gọn P
So sánh p với 3
B=\(\left(\frac{\sqrt{x+1}}{\sqrt{x-1}}+\frac{1-\sqrt{x}}{\sqrt{x+1}}\right):\left(\frac{\sqrt{x+1}}{\sqrt{x-1}}+\frac{\sqrt{x}}{\sqrt{x+1}}+\frac{\sqrt{x}}{1-x}\right)\)
a. Tìm điều kiện xác định,rút gọn B
b. tính B với x= 1- \(\frac{\sqrt{3}}{2}\)
c. so sánh B với 2
Cho \(P=1:\left(\frac{x+2}{x\sqrt{x}+1}+\frac{\sqrt{x}+1}{x+\sqrt{x}+1}-\frac{\sqrt{x}+1}{x-1}\right)\)
a) Rút gọn P
b) So sánh P với 3
Rút gọn
\(1.A=\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3x+3}{x-9}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right)\)
\(2.B=\left(\frac{\sqrt{a}+1}{\sqrt{ab}+1}+\frac{\sqrt{ab}+\sqrt{a}}{\sqrt{ab}-1}-1\right):\left(\frac{\sqrt{a}+1}{\sqrt{ab}+1}-\frac{\sqrt{ab}+\sqrt{a}}{\sqrt{ab}-1}+1\right)\)
\(3.C=\left(\frac{2x-1+\sqrt{x}}{1-x}+\frac{2x\sqrt{x}+x-\sqrt{x}}{1+x\sqrt{x}}\right).\left(\frac{\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)}{2\sqrt{x}-1}\right)\)
\(A:\frac{\sqrt{640}.\sqrt{34,3}}{\sqrt{567}}\)(Rút Gọn)
B:\(M=\left(\frac{1}{x-\sqrt{x}}+\frac{1}{\sqrt{x-1}}\right):\frac{\sqrt{x+1}}{x-2\sqrt{x+1}}\)(rút gọn rồi so sánh giá trị M với 1)
Rút gọn \(M=\left(\frac{2x+3\sqrt{x}}{2\sqrt{x}+1}+\frac{1}{x-\sqrt{x}+1}-\frac{1}{\sqrt{x}+1}\right).\left(\frac{x-\sqrt{x}+1}{\sqrt{x}}\right)\)
Rút gọn các biểu thức sau:
\(B=\frac{\sqrt{1+\sqrt{1-x^2}}[\left(1+x\right)\sqrt{1+x}-\left(1-x\right)\sqrt{1-x}]}{x\left(2+\sqrt{1-x^2}\right)}\)
\(N=\left(\frac{\sqrt{1+x}}{\sqrt{1+x}-\sqrt{1-x}}\frac{1-x}{\sqrt{1-x^2}-1+x}\right).\left(\sqrt{\frac{1}{x^2}-1}-\frac{1-x}{x}\right).\frac{x}{1-x+\sqrt{1-x^2}}\)với -1<x<0
Rút gọn A rồi so sánh với 1
A=\(\left(\frac{1}{\sqrt{x}-1}+\frac{1}{x-\sqrt{x}}\right)\div\frac{\sqrt{x}+1}{x-2\sqrt{x}+1}\)\(\left(x>0,x\ne1\right)\)
\(A=\left(\frac{1}{\sqrt{x}-1}+\frac{1}{x-\sqrt{x}}\right):\frac{\sqrt{x}+1}{x-2\sqrt{x}+1}\)
\(=\left[\frac{\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}+\frac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}\right]:\frac{\sqrt{x}+1}{\left(\sqrt{x}-1\right)^2}\)
\(=\frac{\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-1\right)}.\frac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}+1}=\frac{\sqrt{x}-1}{\sqrt{x}}=1-\frac{1}{\sqrt{x}}< 1\)
a)tìm ĐKXĐ
b)Rút gọn
c) So sánh với 1
\(1:\left(\frac{x+2}{x\sqrt{x}+1}+\frac{\sqrt{x}-1}{x-\sqrt{x}+1}-\frac{\sqrt{x}-1}{x-1}\right)\)
Rút gọn:
\(\left[\frac{2}{3\sqrt{x}}-\frac{2}{\sqrt{x}+1}.\left(\frac{\sqrt{x}+1}{3\sqrt{x}}-\sqrt{x}-1\right)\right]:\frac{\sqrt{x}-1}{\sqrt{x}}\)
với x > 0 và \(x\ne0\)
\(\left[\frac{2}{3\sqrt{x}}-\frac{2}{\sqrt{x}+1}.\left(\frac{\sqrt{x}+1}{3\sqrt{x}}-\sqrt{x}-1\right)\right]:\frac{\sqrt{x}-1}{\sqrt{x}}\)
\(=\left[\frac{2}{3\sqrt{x}}-\frac{2}{\sqrt{x}+1}.\left(\frac{\sqrt{x}+1-3x-3\sqrt{x}}{3\sqrt{x}}\right)\right].\frac{\sqrt{x}}{\sqrt{x}-1}\)
\(=\left[\frac{2}{3\sqrt{x}}-\frac{2}{\sqrt{x}+1}.\frac{-3x-2\sqrt{x}+1}{3\sqrt{x}}\right].\frac{\sqrt{x}}{\sqrt{x}-1}\)
\(=\left[\frac{2}{3\sqrt{x}}-\frac{2}{\sqrt{x}+1}.\frac{\left(\sqrt{x}+1\right)\left(-3\sqrt{x}+1\right)}{3\sqrt{x}}\right].\frac{\sqrt{x}}{\sqrt{x}-1}\)
\(=\left[\frac{2}{3\sqrt{x}}-\frac{-6\sqrt{x}+2}{3\sqrt{x}}\right].\frac{\sqrt{x}}{\sqrt{x}-1}\)
\(=\frac{2\sqrt{x}}{\sqrt{x}-1}\)