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3 tháng 12 2021
Với \(x\ge0;x\ne4;x\ne9\):
\(\Rightarrow B=\dfrac{\sqrt{x}+2}{\sqrt{x}-3}+\dfrac{\sqrt{x}-8}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)
\(=\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)+\left(\sqrt{x}-8\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}\)
\(=\dfrac{x-4+\sqrt{x}-8}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}=\dfrac{\left(\sqrt{x}+4\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}\)
\(=\dfrac{\sqrt{x}+4}{\sqrt{x}-2}\)
4 tháng 12 2021
\(B=\dfrac{x-\sqrt{x}+3+\sqrt{x}-3}{\sqrt{x}\left(\sqrt{x}-3\right)}=\dfrac{\sqrt{x}}{\sqrt{x}-3}\)
16 tháng 4 2023
\(=\dfrac{x+\sqrt{x}-6+x-4\sqrt{x}-12+\sqrt{x}-18}{x-4}\)
\(=\dfrac{2x-2\sqrt{x}-36}{x-4}\)
12 tháng 4 2022
\(B=\dfrac{\sqrt{x}+1}{\sqrt{x}-3}+\dfrac{11\sqrt{x}-3}{x-9}\)
\(B=\dfrac{\sqrt{x}+1}{\sqrt{x}-3}+\dfrac{11\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(B=\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+3\right)+11\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(B=\dfrac{x+3\sqrt{x}+\sqrt{x}+3+11\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(B=\dfrac{x+15\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
16 tháng 7 2021
Ta có: M=A+B
\(=\dfrac{2\sqrt{x}}{\sqrt{x}+3}+\dfrac{\sqrt{x}+1}{\sqrt{x}-3}+\dfrac{11\sqrt{x}-3}{x-9}\)
\(=\dfrac{2x-6\sqrt{x}+x+4\sqrt{x}+3+11\sqrt{x}-3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)
\(=\dfrac{3x+9\sqrt{x}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}=\dfrac{3\sqrt{x}}{\sqrt{x}-3}\)
N
2 tháng 6 2019
ĐK:\(a\ge0;a\ne9\)
\(B=\frac{\sqrt{a}+3}{2\left(\sqrt{a}-3\right)}+\frac{\sqrt{a}-3}{2\left(\sqrt{a}+3\right)}\)
\(=\frac{2\left(\sqrt{a}+3\right)^2+2\left(\sqrt{a}-3\right)^2}{4\left(a-9\right)}\)\(=\frac{a+9}{a-9}\)
31 tháng 10 2022
\(B=\dfrac{a+6\sqrt{a}+9+a-6\sqrt{a}+9}{2\left(a-9\right)}=\dfrac{2a+18}{2a-18}\)
Để B<1 thì B-1<0
=>(2a+18-2a+18)/(2a-18)<0
=>2a-18<0
=>0<=a<9
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