\(\left(\frac{\sqrt{a}}{2}-\frac{1}{2\sqrt{a}}\right)^2\).\(\left(\frac{\sqrt{a}-1}{\sqrt{a}+1}-\frac{\sqrt{a}+1}{\sqrt{a}-1}\right)\)

= \(\left[\left(\frac{\sqrt{a}}{2}\right)^2-2\frac{\sqrt{a}}{2}\frac{1}{2\sqrt{a}}+\left(\frac{1}{2\sqrt{a}}\right)^2\right]\).\(\left[\frac{\left(\sqrt{a}-1\right)\left(\sqrt{a}-1\right)}{a-1}\cdot\frac{\left(\sqrt{a}+1\right)\left(\sqrt{a}+1\right)}{a-1}\right]\)

=\(\left(\frac{a}{4}-\frac{1}{2}+\frac{1}{4a}\right)\).\(\left[\frac{\left(\sqrt{a}-1\right)^2}{a-1}\cdot\frac{\left(\sqrt{a}+1\right)^2}{a-1}\right]\)

=\(\left(\frac{a^2}{4a}-\frac{2a}{4a}+\frac{1}{4a}\right)\).\(\left[\frac{\left[\left(\sqrt{a}-1\right)-\left(\sqrt{a}+1\right)\right]\cdot\left[\left(\sqrt{a}-1\right)+\left(\sqrt{a}+1\right)\right]}{a-1}\right]\)

=\(\left(\frac{a^2-2a+1}{4a}\right)\).\(\left[\frac{\left(\sqrt{a}-1-\sqrt{a}+1\right).\left(\sqrt{a}-1+\sqrt{a}+1\right)}{a-1}\right]\)

=\(\frac{\left(a-1\right)^2}{1}\).\(\frac{-4\sqrt{a}}{a-1}\)

=\(\frac{-\left(a-1\right)}{1}\)= - a + 1

hok tốt 

B ơi b lấy đề này ở đâu v ạ

Bạn có thể đăng từng bài k như thế nhìn đã sợ ai làm

1)đặt nhân tử chung quy đồng là xong

2)phân tích x+2cănx-3=(1-cănx)(3+cănx)

3)2a+căn a đặt căn a ra r rút gọn

\(\frac{a\sqrt{a}-1}{a-\sqrt{a}}-\frac{a\sqrt{a}+1}{a+\sqrt{a}}\)

\(=\frac{\left(a\sqrt{a}-1\right)\left(a+\sqrt{a}\right)-\left(a-\sqrt{a}\right)\left(a\sqrt{a}+1\right)}{\left(a-\sqrt{a}\right)\left(a+\sqrt{a}\right)}\)

\(=\frac{a^2\cdot\sqrt{a}+a^2-a-\sqrt{a}-\left(a^2\sqrt{a}+a-a^2-\sqrt{a}\right)}{a^2-a}\)

\(=\frac{2a^2-2a}{a^2-a}\)

\(=2\)( 1 )

\(\left(\sqrt{a}-\frac{1}{\sqrt{a}}\right)\left(\frac{\sqrt{a}+1}{\sqrt{a}-1}+\frac{\sqrt{a}-1}{\sqrt{a}+1}\right)\)

\(=\left(\frac{\sqrt{a}}{1}-\frac{1}{\sqrt{a}}\right)\left(\frac{\left(\sqrt{a}+1\right)^2+\left(\sqrt{a}-1\right)^2}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\right)\)

\(=\left(\frac{a-1}{\sqrt{a}}\right)\left(\frac{a+2\sqrt{a}+1+a-2\sqrt{a}+1}{a-1}\right)\)

\(=\frac{a-1}{\sqrt{a}}\cdot\frac{2\left(a+1\right)}{a-1}\)

\(=\frac{2\left(a+1\right)}{\sqrt{a}}\) ( 2 )

Cộng ( 1 ) và ( 2 ) lại thì ta được biểu thức ban đầu:

\(2+\frac{2\left(a+1\right)}{\sqrt{a}}\)

Câu b,c em chịu:((

P/S:e ko bt đúng hay sai đâu ạ

Mk giải nốt phần còn lại nha

sai thì thông cảm

\(2+\frac{2\left(a+1\right)}{\sqrt{a}}=7\Leftrightarrow2a+2=5\sqrt{a}\)

\(\Leftrightarrow2a-5\sqrt{a}+2=0\)

\(\Leftrightarrow\left(2\sqrt{a}-1\right)\left(\sqrt{a}-2\right)=0\Rightarrow\orbr{\begin{cases}a=\frac{1}{4}\\a=4\end{cases}}\)

\(2+\frac{2\left(a+1\right)}{\sqrt{a}}>6\)\(\Rightarrow2a+2>4\sqrt{a}\Rightarrow2\left(a+1-2\sqrt{a}\right)>0\)

\(\Leftrightarrow\left(a+1-2\sqrt{a}\right)>0\Leftrightarrow\left(\sqrt{a}-1\right)^2>0\)

\(\Leftrightarrow a\ne1;a\ge0\)

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: \(C=\dfrac{x-9-x+3\sqrt{x}}{x-9}:\left(\dfrac{3-\sqrt{x}}{\sqrt{x}-2}+\dfrac{\sqrt{x}-2}{\sqrt{x}+3}+\dfrac{x-9}{x+\sqrt{x}-6}\right)\)

\(=\dfrac{3\left(\sqrt{x}-3\right)}{x-9}:\dfrac{9-x+x-4\sqrt{x}+4+x-9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}\)

\(=\dfrac{3}{\sqrt{x}+3}\cdot\dfrac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}{x-4\sqrt{x}+4}\)

\(=\dfrac{3}{\sqrt{x}-2}\)

Ai giải giúp mình bài 1 với bài 4 trước đi

\(đkxđ\Leftrightarrow\hept{\begin{cases}a\ge0\\a\ne1\end{cases}}\)

\(A=\)\(\left(\frac{\sqrt{a}}{2}-\frac{1}{2\sqrt{a}}\right)^2\)\(\left(\frac{\sqrt{a}-1}{\sqrt{a}+1}-\frac{\sqrt{a}+1}{\sqrt{a}-1}\right)\)

\(=\left(\frac{\sqrt{a}.\sqrt{a}}{2\sqrt{a}}-\frac{1}{2\sqrt{a}}\right)^2\)\(\left(\frac{\left(\sqrt{a}-1\right)^2}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}-\frac{\left(\sqrt{a}+1\right)^2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right)\)

\(=\left(\frac{a-1}{2\sqrt{a}}\right)^2\left(\frac{\left(\sqrt{a}-1\right)^2-\left(\sqrt{a}+1\right)^2}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\right)\)

\(=\frac{\left(a-1\right)^2}{\left(2\sqrt{a}\right)^2}\left(\frac{a-2\sqrt{a}+1-a-2\sqrt{a}}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right)\)

\(=\frac{\left(a-1\right)^2.-4\sqrt{a}}{4a\left(a-1\right)}=\frac{a-1}{\sqrt{a}}\)

\(b,A< 0\Rightarrow\frac{a-1}{\sqrt{a}}< 0\)

Mà \(\sqrt{a}\ge0\Rightarrow a-1\le0\Rightarrow a\le1\)

\(A=2\Rightarrow\frac{a-1}{\sqrt{a}}=2\)

\(\Rightarrow a-1=2\sqrt{a}\Rightarrow a-2\sqrt{a}-1=0\)

\(\Rightarrow a-2\sqrt{a}+1-2=0\)

\(\Rightarrow\left(\sqrt{a}-1\right)^2-\sqrt{2}^2=0\)

\(\Rightarrow\left(\sqrt{a}-1-\sqrt{2}\right)\left(\sqrt{a}-1+\sqrt{2}\right)=0\)

\(\Rightarrow\orbr{\begin{cases}\sqrt{a}=1+\sqrt{2}\\\sqrt{a}=1-\sqrt{2}\end{cases}\Rightarrow\orbr{\begin{cases}a=\left(1+\sqrt{2}\right)^2=3+2\sqrt{2}\\a=\left(1-\sqrt{2}\right)^2=3-2\sqrt{2}\end{cases}}}\)

\(\left(\frac{\sqrt{a}}{2}-\frac{1}{2\sqrt{a}}\right)^2\left(\frac{\sqrt{a}-1}{\sqrt{a}+1}-\frac{\sqrt{a}+1}{\sqrt{a}-1}\right)\)

\(=\left(\frac{a-1}{2\sqrt{a}}\right)^2\left(\frac{\left(\sqrt{a}-1\right)^2}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}-\frac{\left(\sqrt{a}+1\right)^2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right)\)

\(=\frac{\left(a-1\right)^2}{4a}.\frac{\left(\sqrt{a}-1\right)^2-\left(\sqrt{a}+1\right)^2}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\)

\(=\frac{\left(a-1\right)^2}{4a}.\frac{\left(\sqrt{a}-1+\sqrt{a}+1\right)\left(\sqrt{a}-1-\sqrt{a}-1\right)}{a-1}\)

\(=\frac{a-1}{4a}.\frac{2\sqrt{a}.\left(-2\right)}{1}\)

\(=\frac{a-1}{4a}.\frac{-4\sqrt{a}.}{1}\)

\(=\frac{1-a}{\sqrt{a}}\)