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5: \(=\dfrac{1}{x-y}\cdot x^3\cdot\left(x-y\right)^2=x^3\left(x-y\right)\)
Bài 1:
a: Ta có: \(x^2-2\sqrt{5}x+5=0\)
\(\Leftrightarrow x-\sqrt{5}=0\)
hay \(x=\sqrt{5}\)
b: Ta có: \(\sqrt{x+3}=1\)
\(\Leftrightarrow x+3=1\)
hay x=-2
a: Ta có: \(A=\dfrac{x^2+\sqrt{x}}{x-\sqrt{x}+1}-\dfrac{2x+\sqrt{x}}{\sqrt{x}}+1\)
\(=\sqrt{x}\left(\sqrt{x}+1\right)-\left(2\sqrt{x}+1\right)+1\)
\(=x+\sqrt{x}-2\sqrt{x}-1+1\)
\(=x-\sqrt{x}\)
b: Ta có: \(A=\dfrac{\sqrt{x}+2}{\sqrt{x}+3}+\dfrac{5}{x+\sqrt{x}-6}+\dfrac{1}{2-\sqrt{x}}\)
\(=\dfrac{x-4+5-\sqrt{x}-3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}\)
\(=\dfrac{x-\sqrt{x}-2}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}=\dfrac{\sqrt{x}+1}{\sqrt{x}+3}\)
Sửa đề: căn x-5/căn x-3
a: \(A=\left(\dfrac{\sqrt{x}}{\sqrt{x}+5}-1\right):\dfrac{25-x-x+9+x-25}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-3\right)}\)
\(=\dfrac{\sqrt{x}-\sqrt{x}-5}{\sqrt{x}+5}\cdot\dfrac{\left(\sqrt{x}+5\right)\left(\sqrt{x}-3\right)}{-\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}=\dfrac{5}{\sqrt{x}+3}\)
b: x-5căn x+6=0
=>căn x=2 hoặc căn x=3
=>x=9(loại) hoặc x=4(nhận)
Khi x=4 thì A=5/(2+3)=5/5=1
Ta có: \(A=\dfrac{\sqrt{x}}{\sqrt{x}-3}+\dfrac{2\sqrt{x}-1}{\sqrt{x}-3}-\dfrac{2x-\sqrt{x}-3}{x-9}\)
\(=\dfrac{x-3\sqrt{x}+2x-6\sqrt{x}-\sqrt{x}+3-2x+\sqrt{x}+3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{x-9\sqrt{x}+6}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
a) Ta có: \(\dfrac{x+\sqrt{5}}{x^2+2x\sqrt{5}+5}\)
\(=\dfrac{x+\sqrt{5}}{\left(x+\sqrt{5}\right)^2}=\dfrac{1}{x+\sqrt{5}}\)
b) Ta có: \(B=\dfrac{a-2\sqrt{a}-3}{a-9}\)
\(=\dfrac{\left(\sqrt{a}-3\right)\left(\sqrt{a}+1\right)}{\left(\sqrt{a}-3\right)\left(\sqrt{a}+3\right)}\)
\(=\dfrac{\sqrt{a}+1}{\sqrt{a}+3}\)
c) Ta có: \(C=\sqrt{x-1-2\sqrt{x-2}}\)
\(=\sqrt{x-2-2\cdot\sqrt{x-2}\cdot1+1}\)
\(=\sqrt{\left(\sqrt{x-2}-1\right)^2}\)
\(=\left|\sqrt{x-2}-1\right|\)
`a)A=(x+sqrt5)(x^2+2xsqrt5+5)`
`=(x+sqrt5)/(x+sqrt5)^2=1/(x+sqrt5)`
`b)B=(a-2sqrta-3)/(a-9)(a>=0,a ne 9)`
`=(a+sqrta-3sqrta-3)/(a-9)`
`=((sqrta+1)(sqrta-3))/((sqrta-3)(sqrta+3))`
`=(sqrta+1)/(sqrta+3)`
`c)C=sqrt{x-1-2sqrt{x-2}}(x>=2)`
`=sqrt{x-2-2sqrt{x-2}+1}`
`=sqrt{(sqrt{x-2}-1)^2}`
`=|sqrt(x-2)-1|`
1) Ta có: \(\dfrac{a-6\sqrt{a}+9}{5\sqrt{a}-15}\)
\(=\dfrac{\left(\sqrt{a}-3\right)^2}{5\left(\sqrt{a}-3\right)}\)
\(=\dfrac{\sqrt{a}-3}{5}\)
2) Ta có: \(5x-\sqrt{x^2-10x+25}\)
\(=5x-\left|x-5\right|\)
\(=5x-5+x\)
=6x-5
3) Ta có: \(\dfrac{\sqrt{x^2-2x+1}}{x-1}\)
\(=\dfrac{\left|x-1\right|}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{\pm1}{x+1}\)
4) Ta có: \(3\sqrt{5}-\sqrt{46-6\sqrt{5}}\)
\(=3\sqrt{5}-3\sqrt{5}+1\)
=1