a) ĐKXĐ: \(\dfrac{2x+1}{x^2+1}\ge0\Leftrightarrow2x+1\ge0\Leftrightarrow x\ge-\dfrac{1}{2}\)

b) \(\sqrt[3]{-27}+\sqrt[3]{64}-\dfrac{\sqrt[3]{-128}}{\sqrt[3]{2}}=-3+4-\sqrt[3]{-64}=1+4=5\)

a: ĐKXĐ: \(x\ge-\dfrac{1}{2}\)

b: Ta có: \(\sqrt[3]{-27}+\sqrt[3]{64}-\dfrac{\sqrt[3]{-128}}{\sqrt[3]{2}}\)

\(=-3+4-\left(-4\right)\)

=-3+4+4

=5

1) \(ĐK:3-2a>0\Leftrightarrow a< \dfrac{3}{2}\)

2) \(ĐK:2x-5< 0\Leftrightarrow x< \dfrac{5}{2}\)

3) \(ĐK:3-5a< 0\Leftrightarrow a>\dfrac{3}{5}\)

4) \(ĐK:a< 0\)

5) \(ĐK:-a\ge0\Leftrightarrow a\le0\)

a: ĐKXĐ: 5-4x>=0

=>x<=5/4

b: ĐKXĐ: x thuộc R

c: ĐKXĐ: x-2<0

=>x<2

\(a,ĐK:5-4x\ge0\\ \Rightarrow x\le\dfrac{5}{4}\\ b,ĐK:\left(x+1\right)^2\ge0\left(lđ\right)\)

\(\Rightarrow\) Với mọt giá trị của x

\(c,ĐK:\dfrac{-1}{x-2}\ge0\)

Vì \(-1< 0\)

\(\Rightarrow x-2< 0\)

\(\Rightarrow x< 2\)

a)

Căn thức có nghĩa thì:

 \(5-4x\ge0\\ \Leftrightarrow4x\le5\\ \Rightarrow x\le\dfrac{5}{4}\)

b)

Để căn thức có nghĩa thì:

\(\left(x+1\right)^2\ge0\) (luôn đúng)

Vậy căn thức có nghĩa với mọi giá trị x.

c)

Để căn thức có nghĩa thì:

\(\left\{{}\begin{matrix}-\dfrac{1}{x-2}\ge0\\x-2\ne0\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x-2< 0\\x\ne2\end{matrix}\right.\\ \Rightarrow x< 2\)

Bài 1 :

a, ĐKXĐ : \(\dfrac{1}{2-x}\ge0\)

Mà 1 > 0

\(\Rightarrow2-x>0\)

\(\Rightarrow x< 2\)

Vậy ...

b, Ta có : \(\sqrt[3]{125}.\sqrt[3]{216}-\sqrt[3]{512}.\sqrt[3]{\dfrac{1}{8}}\)

\(=5.6-\dfrac{8.1}{2}=26\)

1a) Để căn thức bậc 2 có nghĩa thì \(\dfrac{1}{2-x}\ge0\Rightarrow2-x>0\Rightarrow x< 2\)

b) \(\sqrt[3]{125}.\sqrt[3]{-216}-\sqrt[3]{512}.\sqrt[3]{\dfrac{1}{8}}=\sqrt[3]{5^3}.\sqrt[3]{\left(-6\right)^3}-\sqrt[3]{8^3}.\sqrt[3]{\left(\dfrac{1}{2}\right)^3}\)

\(=5.\left(-6\right)-8.\dfrac{1}{2}=-34\)

\(\dfrac{\sqrt{ab}-b}{b}-\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)}{\left(\sqrt{b}\right)^2}-\dfrac{\sqrt{a}}{\sqrt{b}}=\dfrac{\sqrt{a}-\sqrt{b}}{\sqrt{b}}-\dfrac{\sqrt{a}}{\sqrt{b}}\)

\(=-\dfrac{\sqrt{b}}{\sqrt{b}}=-1< 0\)

a: ĐKXĐ: b>=0; b<>1

\(B=\dfrac{1-\sqrt{b}+1+\sqrt{b}}{2\left(1-b\right)}-\dfrac{b^2+1}{1-b^2}\)

\(=\dfrac{1}{1-b}+\dfrac{b^2+1}{b^2-1}\)

\(=\dfrac{-b-1+b^2+1}{b^2-1}=\dfrac{b\left(b-1\right)}{\left(b-1\right)\left(b+1\right)}=\dfrac{b}{b+1}\)

b: B>1/3

=>B-1/3>0

=>b/b+1-1/3>0

=>(3b-b-1)/(3b+3)>0

=>2b-1>0

=>b>1/2

ĐKXĐ: \(\left\{{}\begin{matrix}x>0\\x\ne1\end{matrix}\right.\)

a: ĐKXĐ: \(x>0\)

b: Ta có: \(A=\dfrac{x^2+\sqrt{x}}{x-\sqrt{x}+1}-\dfrac{2x+\sqrt{x}}{\sqrt{x}}+1\)

\(=x+\sqrt{x}-2\sqrt{x}-1+1\)

\(=x-\sqrt{x}\)

\(a,\)

\(=\left(\dfrac{\sqrt{x}-1}{3\sqrt{x}-1}-\dfrac{1}{3\sqrt{x}+1}+\dfrac{8\sqrt{x}}{\left(3\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)}\right):\left(\dfrac{3\sqrt{x}+1-3\sqrt{x}+2}{3\sqrt{x}+1}\right)\)

\(=\left(\dfrac{\left(\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)-3\sqrt{x}+1+8\sqrt{x}}{\left(3\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)}\right):\left(\dfrac{3}{3\sqrt{x}+1}\right)\)

\(=\dfrac{3x+\sqrt{x}-3\sqrt{x}-1-3\sqrt{x}+1+8\sqrt{x}}{\left(3\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)}.\dfrac{3\sqrt{x}+1}{3}\)

\(=\dfrac{3\sqrt{x}+3x}{\left(3\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)}.\dfrac{3\sqrt{x}+1}{3}\)

\(=\dfrac{3\sqrt{x}\left(\sqrt{x}+1\right)}{\left(3\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)}.\dfrac{3\sqrt{x}+1}{3}\)

\(=\dfrac{3\sqrt{x}+1}{3\sqrt{x}-1}\)

Vậy \(P=\dfrac{3\sqrt{x}+1}{3\sqrt{x}-1}\)

\(b,\)Thay \(P=\dfrac{6}{5}\) vào pt, ta có :

\(\dfrac{3\sqrt{x}+1}{3\sqrt{x}-1}=\dfrac{6}{5}\)

\(\Leftrightarrow5\left(3\sqrt{x}+1\right)=6\left(3\sqrt{x}-1\right)\)

\(\Leftrightarrow15\sqrt{x}+5-18\sqrt{x}+6=0\)

\(\Leftrightarrow-3\sqrt{x}+11=0\)

\(\Leftrightarrow-3\sqrt{x}=-11\)

\(\Leftrightarrow\sqrt{x}=\dfrac{11}{3}\)

\(\Leftrightarrow x=\left(\dfrac{11}{3}\right)^2\)

\(\Leftrightarrow x=\dfrac{121}{9}\)

Vậy \(x=\dfrac{121}{9}\) thì \(P=\dfrac{6}{5}\)