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13 tháng 7 2021
a) Ta có: \(A=\left(\dfrac{a\sqrt{a}-1}{a-\sqrt{a}}-\dfrac{a\sqrt{a}+1}{a+\sqrt{a}}\right):\dfrac{a+2}{a-2}\)
\(=\left(\dfrac{a+\sqrt{a}+1-\left(a-\sqrt{a}+1\right)}{\sqrt{a}}\right):\dfrac{a+2}{a-2}\)
\(=2\cdot\dfrac{a-2}{a+2}\)
\(=\dfrac{2a-4}{a+2}\)
VQ
1
6 tháng 7 2021
Ta có: \(P=\dfrac{\sqrt{x}+1}{x-1}-\dfrac{x+2}{x\sqrt{x}-1}-\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}\)
\(=\dfrac{x+\sqrt{x}+1-x-2-\left(x-1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\dfrac{\sqrt{x}-1-x+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\dfrac{-\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\dfrac{-\sqrt{x}}{x+\sqrt{x}+1}\)
6 tháng 7 2021
Ta có: \(P=1:\left(\dfrac{x+2}{x\sqrt{x}-1}+\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}-\dfrac{\sqrt{x}+1}{x-1}\right)\)
\(=1:\left(\dfrac{x+2}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}+\dfrac{x-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}-\dfrac{x+\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\right)\)
\(=1:\dfrac{x+2+x-1-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=1:\dfrac{x-\sqrt{x}}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\dfrac{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}\)
\(=\dfrac{x+\sqrt{x}+1}{\sqrt{x}}\)
5 tháng 1 2022
\(B=\dfrac{2\sqrt{x}-6\sqrt{x}+x+3\sqrt{x}-3x-9}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{-3\left(\sqrt{x}+3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}=\dfrac{-3}{\sqrt{x}-3}\)
5 tháng 1 2022
\(B=\dfrac{2x-6\sqrt{x}+x+3\sqrt{x}-3x-9}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}=\dfrac{3\sqrt{x}-9}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\\ B=\dfrac{3\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}=\dfrac{3}{\sqrt{x}+3}\)
MB
1
30 tháng 9 2021
\(\dfrac{x-2\sqrt{x}}{x-4}=\dfrac{\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\dfrac{\sqrt{x}}{\sqrt{x}+2}\)
7 tháng 12 2021
\(a,A=2\sqrt{3}+10\sqrt{3}-5\sqrt{3}=7\sqrt{3}\\ b,ĐK:x\ge0\\ PT\Leftrightarrow x^2-2x+1+x-2\sqrt{x}+1=0\\ \Leftrightarrow\left(x-1\right)^2+\left(\sqrt{x}-1\right)^2=0\\ \Leftrightarrow\left\{{}\begin{matrix}x=1\\\sqrt{x}=1\end{matrix}\right.\Leftrightarrow x=1\left(tm\right)\)
NT
3
19 tháng 8 2021
\(P=\left(\frac{1}{\sqrt{x}}+\frac{\sqrt{x}}{\sqrt{x}+1}\right):\frac{\sqrt{x}}{x+\sqrt{x}}\)ĐK : x > 0
\(=\left(\frac{\sqrt{x}+1+x}{\sqrt{x}\left(\sqrt{x}+1\right)}\right):\frac{1}{\sqrt{x}+1}=\frac{x+\sqrt{x}+1}{\sqrt{x}}\)
\(P=\frac{\sqrt{x}}{\sqrt{x}-1}+\frac{3}{\sqrt{x}+1}-\frac{6\sqrt{x}-4}{x-1}\)
\(=\frac{x+\sqrt{x}+3\sqrt{x}-3-6\sqrt{x}+4}{x-1}=\frac{x-2\sqrt{x}+1}{x-1}=\frac{\sqrt{x}-1}{\sqrt{x}+1}\)
AH
Akai Haruma
Giáo viên
5 tháng 10 2021
1. ĐKXĐ: $x\geq 1$
PT $\Leftrightarrow \sqrt{x-1}=13-x$
\(\Rightarrow \left\{\begin{matrix} 13-x\geq 0\\ x-1=(13-x)^2\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x\leq 13\\ x^2-27x+170=0\end{matrix}\right.\)
\(\Leftrightarrow \left\{\begin{matrix} x\leq 13\\ (x-17)(x-10)=0\end{matrix}\right.\)
\(\Rightarrow x=10\) (tm)
AH
Akai Haruma
Giáo viên
5 tháng 10 2021
2. ĐKXĐ: $x\geq 3$
\(3\sqrt{x+34}-3\sqrt{x-3}=1\)
\(\Leftrightarrow 3\sqrt{x+34}=3\sqrt{x-3}+1\)
\(\Rightarrow 9(x+34)=9x+6\sqrt{x-3}-26\)
\(\Leftrightarrow \frac{166}{3}=\sqrt{x-3}\)
$\Leftrightarrow x-3=\frac{27556}{9}$
$\Leftrightarrow x=\frac{27583}{9}$ (tm)
NH
1
9 tháng 10 2021
Bài 7:
Ta có: \(P=\left(\dfrac{2\sqrt{x}}{x\sqrt{x}+\sqrt{x}-x-1}\right):\left(1+\dfrac{\sqrt{x}}{x+1}\right)\)
\(=\dfrac{2\sqrt{x}}{\left(x+1\right)\left(\sqrt{x}-1\right)}\cdot\dfrac{x+1}{x+\sqrt{x}+1}\)
\(=\dfrac{2\sqrt{x}}{x\sqrt{x}-1}\)
`P=(1+5/(sqrtx-2)).(sqrtx-(x+2sqrtx+4)/(sqrtx+3))`
`=((sqrtx-2+5)/(sqrtx-2)).((x+3sqrtx-x-2sqrtx-4)/(sqrtx+3))`
`=(sqrtx+3)/(sqrtx-2).(sqrtx-4)/(sqrtx+3)`
`=(sqrtx-4)/(sqrtx-2)`