\(a,2x+3>0\\ 2x>-3\\ x>-\dfrac{3}{2}\\ b,x+1< 0\\ x< -1\\ c,x>-2\\ d,x>2\)
e, x ≠ 3
`a)`\(\sqrt{\dfrac{4}{2x+3}}=\dfrac{\sqrt{4}}{\sqrt{2x+3}}=\dfrac{2}{\sqrt{2x+3}}\)
\(ĐK:x>-\dfrac{3}{2}\)
`b)`\(\sqrt{-\dfrac{2}{x+1}}=\dfrac{\sqrt{2}}{\sqrt{-x-1}}\)
\(ĐK:x\le-1\)
`c)`\(\dfrac{x}{x+2}+\sqrt{x+2}\)
\(ĐK:x\ne-2\)
\(x\ge-2\)
\(\Rightarrow x>-2\)
`d)`\(\dfrac{x}{x^2-4}+\sqrt{x-2}=\dfrac{x}{\left(x-2\right)\left(x+2\right)}+\sqrt{x-2}\)
\(ĐK:x\ne\pm2\)
\(x\ge2\)
\(\Rightarrow x>2\)
`e)`\(\sqrt{9x^2-6x+1}=\sqrt{\left(3x-1\right)^2}\)
\(ĐK:x\in R\)
a) \(\sqrt{\dfrac{4}{2x+3}}\)
`ĐKXĐ : 2x+3 > 0`
`<=> 2x > -3`
`<=> x > -3/2`
b)\(\sqrt{-\dfrac{2}{x+1}}\)
ĐKXĐ : `x+1 <0`
`<=> x < -1 `
c)\(\dfrac{x}{x+2}+\sqrt{x+2}\)
ĐKXĐ : ` x+2>0`
`<=> x>-2`
d)\(\dfrac{x}{x^2-4}+\sqrt{x-2}=\dfrac{x}{\left(x+2\right)\left(x-2\right)}+\sqrt{x-2}\)
ĐK : \(\left\{{}\begin{matrix}x\ne\pm2\\x\ge-2\end{matrix}\right.\)
e)\(\sqrt{9x^2-6x+1}=\sqrt{9x^2-3x-3x+1}\)
\(=\sqrt{3x\left(3x-1\right)-\left(3x-1\right)}=\sqrt{\left(3x-1\right)^2}\)
ĐKXĐ : `x∈R`