Bài 9 :
\(a,\) \(x=25\Rightarrow A=\dfrac{2\sqrt{25}}{\sqrt{25}+3}=\dfrac{2.5}{5+3}=\dfrac{10}{8}=\dfrac{5}{4}\)
\(b,M=A+B=\dfrac{2\sqrt{x}}{\sqrt{x}+3}+\dfrac{\sqrt{x}+1}{\sqrt{x}-3}+\dfrac{11\sqrt{x}-3}{x-9}\left(dkxd:x\ge0,x\ne9\right)\)
\(=\dfrac{2\sqrt{x}}{\sqrt{x}+3}+\dfrac{\sqrt{x}+1}{\sqrt{x}-3}+\dfrac{11\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{2\sqrt{x}\left(\sqrt{x}-3\right)+\left(\sqrt{x}+1\right)\left(\sqrt{x}+3\right)+11\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{2x-6\sqrt{x}+x+3\sqrt{x}+\sqrt{x}+3+11\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{3x+9\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{3\sqrt{x}\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{3\sqrt{x}}{\sqrt{x}-3}\)
Bài 10 :
\(a,x=4\Rightarrow A=\dfrac{4-\sqrt{4}}{4-1}=\dfrac{4-2}{3}=\dfrac{2}{3}\)
\(b,A=\dfrac{x-\sqrt{x}}{x-1}=\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{\sqrt{x}}{\sqrt{x}+1}\)
\(B=\dfrac{x-4}{x+2\sqrt{x}}=\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\sqrt{x}\left(\sqrt{x}+2\right)}=\dfrac{\sqrt{x}-2}{\sqrt{x}}\)
\(c,\) \(\dfrac{\sqrt{x}}{\sqrt{x}+1}>\dfrac{\sqrt{x}-2}{\sqrt{x}}\Rightarrow A>B\)
12:
a: Khi x=1 thì B=1/(1-3)=1/(-2)=-1/2
b: S=A-B
\(=\dfrac{x+3+2\sqrt{x}-6-\sqrt{x}-3}{x-9}=\dfrac{x+\sqrt{x}-6}{x-9}=\dfrac{\sqrt{x}-2}{\sqrt{x}-3}\)
c: S=(căn x+1)/(căn x-2)
=>(căn x-2)/(căn x-3)=(căn x+1)/(căn x-2)
=>x-4căn x+4=x-2căn x-3
=>-2căn x=-7
=>x=49/4
