tim dkxd \(\sqrt{x}+3\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Để \(\sqrt{x}-1\) được xác định cần:
\(\sqrt{x}\ge0\)
<=> \(x\ge0\)
Vậy ĐKXĐ của \(\sqrt{x}-1\) là \(x\ge0\)
![](https://rs.olm.vn/images/avt/0.png?1311)
ĐKXĐ: \(\orbr{\begin{cases}x>\sqrt{2}+1\\\frac{-1}{2}\le x< 1-\sqrt{2}\end{cases}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{\sqrt{x}+1}{\sqrt{x}\left(x+\sqrt{x}+1\right)}.\frac{\sqrt{x}\left(\sqrt{x^3}-1\right)}{1}\)
\(A=\frac{\sqrt{x}+1}{\sqrt{x}\left(x+\sqrt{x}+1\right)}.\sqrt{x}\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)\)
\(A=\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)
\(A=x-1\)
(ĐKXĐ là: \(x>0;x\ne1\))
![](https://rs.olm.vn/images/avt/0.png?1311)
sữa đề chút
a) đkxđ : \(x>2;x\ne3\)
b) ta có : \(A=\dfrac{\sqrt{x-1-2\sqrt{x-2}}}{\sqrt{x-2}-1}=\dfrac{\sqrt{\left(\sqrt{x-2}-1\right)^2}}{\sqrt{x-2}-1}=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
ĐKXĐ: (1-x)(2x-1)>=0
\(\Rightarrow\hept{\begin{cases}1-x>=0\\2\text{x}-1>=0\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x\le1\\x\ge\frac{1}{2}\end{cases}}\)
vậy 1/2<=x<=1
bé hơn hoặc bằng nha
![](https://rs.olm.vn/images/avt/0.png?1311)
ĐKXĐ : \(2x-x^2-3\ne0\Rightarrow-x^2+2x-3\ne0\)
\(\Rightarrow-\left(x^2-2x+3\right)\ne0\Rightarrow x^2-2.x+1+2\ne0\)
\(\Rightarrow\left(x-1\right)^2+2\ne0\)
VÌ \(\left(x-1\right)^2\ge0\) dấu = khi x=1
\(2>0\)
\(\Rightarrow\left(x-1\right)^2+2>0\)
\(\Rightarrow\left(x-1\right)^2+2\ne0\) luôn đúng
\(\Rightarrow2x-x^2-3\ne0\) luôn đúng
\(\Rightarrow\text{Đ}K\text{X}\text{Đ}:x\in R\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a ) ĐK : \(\left\{{}\begin{matrix}x\ge0\\x\ne1\end{matrix}\right.\)\(P=\left(\dfrac{1}{\sqrt{x}+1}-\dfrac{2\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+1\right)^{^2}\left(\sqrt{x}-1\right)}\right):\left(\dfrac{1}{\sqrt{x}-1}+\dfrac{2}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right)\)
\(=\dfrac{x-1-2\sqrt{x}+2}{\left(\sqrt{x}+1\right)^2\left(\sqrt{x}-1\right)}:\dfrac{\sqrt{x}+3}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}+1\right)^2\left(\sqrt{x}-1\right)}.\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{\sqrt{x}+3}\)
\(=\dfrac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}+1\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{x-2\sqrt{x}+1}{x+4\sqrt{x}+3}\)
ĐKXĐ: \(x\ge0\)
ĐKXĐcủa√x+3=x≥0