Cho B = \(\frac{\sqrt{x}}{\sqrt{x}-1}\)+ \(\frac{3}{\sqrt{x}+1}\)-\(\frac{6\sqrt{x}-4}{x-1}\)
a) Rút gọn B
b) Tìm x để B< \(\frac{1}{2}\)
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T
12 tháng 8 2019
giải thử thôi nha
a) \(P=\frac{\sqrt{x}}{\sqrt{x}-1}+\frac{3}{\sqrt{x}+1}-\frac{6\sqrt{x}-4}{x-1}\)
\(=\frac{\sqrt{x}\left(x-1\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(x-1\right)\left(\sqrt{x}+1\right)}+\frac{3\left(x-1\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+1\right)\left(x-1\right)\left(\sqrt{x}-1\right)}-\frac{\left(6\sqrt{x}-4\right)\left(\sqrt{x}-1\right)\left(\sqrt{x+1}\right)}{\left(x-1\right)\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{x^2-2x\sqrt{x}+2\sqrt{x}-1}{\left(x-1\right)\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{x^2-2x\sqrt{x}+2\sqrt{x}-1}{\left(x-1\right)^2}\)
12 tháng 8 2019
a, ĐKXĐ: \(x\ne1;x\ge0\)\(P=\frac{\sqrt{x}}{\sqrt{x}-1}+\frac{3}{\sqrt{x}+1}-\frac{6\sqrt{x}-4}{x-1}\)
\(=\frac{\sqrt{x}\left(\sqrt{x}+1\right)}{x-1}+\frac{3\left(\sqrt{x}-1\right)}{x-1}-\frac{6\sqrt{x}-4}{x-1}\)
\(=\frac{x+\sqrt{x}+3\sqrt{x}-3-6\sqrt{x}+4}{x-1}\)
\(=\frac{x-2\sqrt{x}+1}{x-1}\)
\(=\frac{\left(\sqrt{x}-1\right)^2}{x-1}\)\(=\frac{\sqrt{x}-1}{\sqrt{x}+1}\)
5 tháng 2 2022
a: \(A=\dfrac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\sqrt{a}-\sqrt{b}}-\dfrac{\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{ab}}\)
\(=\sqrt{a}-\sqrt{b}-\sqrt{a}-\sqrt{b}=-2\sqrt{b}\)
b: \(B=\dfrac{2\sqrt{x}-x-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\cdot\dfrac{x+\sqrt{x}+1}{x-1}\)
\(=\dfrac{-2x+\sqrt{x}-1}{\sqrt{x}-1}\cdot\dfrac{1}{x-1}\)
c: \(C=\dfrac{x-9-x+3\sqrt{x}}{x-9}:\left(\dfrac{3-\sqrt{x}}{\sqrt{x}-2}+\dfrac{\sqrt{x}-2}{\sqrt{x}+3}+\dfrac{x-9}{x+\sqrt{x}-6}\right)\)
\(=\dfrac{3\left(\sqrt{x}-3\right)}{x-9}:\dfrac{9-x+x-4\sqrt{x}+4+x-9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}\)
\(=\dfrac{3}{\sqrt{x}+3}\cdot\dfrac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}{x-4\sqrt{x}+4}\)
\(=\dfrac{3}{\sqrt{x}-2}\)
2 tháng 2 2022
a: \(A=\dfrac{1}{\sqrt{x}+1}:\left(\dfrac{x-9-x+4+\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\right)\)
\(=\dfrac{1}{\sqrt{x}+1}\cdot\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}{\sqrt{x}-3}\)
\(=\dfrac{\sqrt{x}-2}{\sqrt{x}+1}\)
b: Để A<0 thì \(\sqrt{x}-2< 0\)
hay 0<x<4