B= (2sqrt(x))/(x - 9) - 2 sqrt x +3 (x>0,x ne9).
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cho biểu thức B=(1/(sqrt(x) + 3) + (2sqrt(x))/(x - 9) ) 2 sqrt x +6 sqrt x -1 với x >= 0 x ne1;x ne9 a) rút gọn B
\(B=\left(\dfrac{1}{\sqrt{x}+3}+\dfrac{2\sqrt{x}}{x-9}\right)\cdot\dfrac{2\sqrt{x}+6}{\sqrt{x}-1}\)
\(=\dfrac{\sqrt{x}-3+2\sqrt{x}}{x-9}\cdot\dfrac{2\left(\sqrt{x}+3\right)}{\sqrt{x}-1}\)
\(=\dfrac{3\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\cdot\dfrac{2}{\sqrt{x}-3}=\dfrac{6}{\sqrt{x}-3}\)
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P = (sqrt(x))/(sqrt(x) + 3) / ((2sqrt(x))/(sqrt(x) - 3)) - (3x + 9)/(x - 9) ,x>=0.4x ne9.
\(P=\dfrac{\sqrt{x}}{\sqrt{x}+3}:\dfrac{2\sqrt{x}}{\sqrt{x}-3}-\dfrac{3x+9}{x-9}\)
\(=\dfrac{\sqrt{x}-3}{2\left(\sqrt{x}+3\right)}-\dfrac{3x+9}{x-9}\)
\(=\dfrac{x-9-3x-9}{2\left(x-9\right)}=\dfrac{-2x-18}{2\left(x-9\right)}=\dfrac{-x-9}{x-9}\)
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Cho A = 6/(x - 3sqrt(x)) B= (2sqrt(x))/(x - 9) - 2 sqrt x +3 (x>0,x ne9) a) Tính giá trị của A khi x = 16 b) Rút gọn biểu thức P = A/B c) So sánh P với 1. d) Tính x biết P * sqrt(x) >= x/4 + 4
a: Khi x=16 thì \(A=\dfrac{6}{16-3\cdot4}=\dfrac{6}{4}=\dfrac{3}{2}\)
b: P=A:B
\(=\dfrac{6}{\sqrt{x}\left(\sqrt{x}-3\right)}:\dfrac{2\sqrt{x}-2\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{6}{\sqrt{x}\left(\sqrt{x}-3\right)}\cdot\dfrac{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}{6}\)
\(=\dfrac{\sqrt{x}+3}{\sqrt{x}}\)
c: \(P-1=\dfrac{\sqrt{x}+3-\sqrt{x}}{\sqrt{x}}=\dfrac{3}{\sqrt{x}}>0\)
=>P>1
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\(B=\dfrac{2\sqrt{x}}{\sqrt{x}+3}+\dfrac{x+9\sqrt{x}}{9-x};\left(x\ge0;x\ne9;x\ne16\right)\)
\(B=\dfrac{3}{\sqrt{x}-3}+\dfrac{2}{\sqrt{x}+3}+\dfrac{x-5\sqrt{x}-3}{x-9}\)
\(B=\dfrac{\sqrt{x}+1}{\sqrt{x}-1}-\dfrac{x+\sqrt{x}}{x-1};\left(x>0;x\ne1\right)\)
1.
\(A=\dfrac{2\sqrt{x}}{\sqrt{x}+3}+\dfrac{x+9\sqrt{x}}{9-x}\)
\(=\dfrac{2\sqrt{x}}{\sqrt{x}+3}-\dfrac{x+9\sqrt{x}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)
\(=\dfrac{2\sqrt{x}\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}-\dfrac{x+9\sqrt{x}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)
\(=\dfrac{2x-6\sqrt{x}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}-\dfrac{x+9\sqrt{x}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)
\(=\dfrac{x-15\sqrt{x}}{x-9}\)
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2.
\(B=\dfrac{3}{\sqrt{x}-3}+\dfrac{2}{\sqrt{x}+3}+\dfrac{x-5\sqrt{x}-3}{x-9}\)
\(=\dfrac{3\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}+\dfrac{2\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}+\dfrac{x-5\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{3\sqrt{x}+9+2\sqrt{x}-6+x-5\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{x}{x-9}\)
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3.
\(C=\dfrac{\sqrt{x}+1}{\sqrt{x}-1}-\dfrac{x+\sqrt{x}}{x-1}\)
\(=\dfrac{\sqrt{x}+1}{\sqrt{x}-1}-\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{\sqrt{x}+1}{\sqrt{x}-1}-\dfrac{\sqrt{x}}{\sqrt{x}-1}\)
\(=\dfrac{1}{\sqrt{x}-1}\)
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Xem thêm câu trả lời
Cho biểu thức P = ((2sqrt(x))/(sqrt(x) + 3) + (sqrt(x))/(sqrt(x) - 3) - (3x + 3)/(x - 9)) / ((2sqrt(x) - 2)/(sqrt(x) - 3) - 1) Tổng các giá trị nguyên của x để P
\(P=\dfrac{2\sqrt{x}}{\sqrt{x}+3}+\dfrac{\sqrt{x}}{\sqrt{x}-3}-\dfrac{3x+3}{x-9}:\dfrac{2\sqrt{x}-2-\sqrt{x}+3}{\sqrt{x}-3}\)
\(=\dfrac{2x-6\sqrt{x}+x+3\sqrt{x}}{x-9}+\dfrac{3x+3}{x-9}\cdot\dfrac{\sqrt{x}+3}{\sqrt{x}+1}\)
\(=\dfrac{\left(3x-3\sqrt{x}\right)\left(\sqrt{x}+1\right)+\left(3x+3\right)\left(\sqrt{x}+3\right)}{\left(x-9\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{3x\sqrt{x}+3x-3x-3\sqrt{x}+3x\sqrt{x}+9x+3\sqrt{x}+9}{\left(x-9\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{6x\sqrt{x}+9x+9}{\left(x-9\right)\left(\sqrt{x}+1\right)}\)
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\(B=\left(\dfrac{3}{x-3\sqrt{x}}+\dfrac{1}{\sqrt{x}+3}\right)\times\dfrac{x-9}{\sqrt{x}}\left(x>0;x\ne9\right)\)
\(=\dfrac{3\sqrt{x}+9+x-3\sqrt{x}}{\sqrt{x}\left(x-9\right)}\cdot\dfrac{x-9}{\sqrt{x}}=\dfrac{x+9}{x}\)
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Gidipt 1) sqrt(x ^ 2 - x) = sqrt(3 - x)
2) sqrt(x ^ 2 - 4x + 3) = x - 2
3) sqrt(4 * (1 - x) ^ 2) - 6 = 0
4) sqrt(x ^ 2 - 4x + 4) = sqrt(4x ^ 2 - 12x + 9)
5) sqrt(x ^ 2 - 4) + sqrt(x ^ 2 + 4x + 4) = 0
6) 1sqrt(x + 2sqrt(x - 1)) + sqrt(x - 2sqrt(x - 1)) = 2
1: =>x^2-x=3-x
=>x^2=3
=>x=căn 3 hoặc x=-căn 3
2: =>x^2-4x+3=x^2-4x+4 và x>=2
=>3=4(vô lý)
3: =>2|x-1|=6
=>|x-1|=3
=>x-1=3 hoặc x-1=-3
=>x=-2 hoặc x=4
4: =>|2x-3|=|x-2|
=>2x-3=x-2 hoặc 2x-3=-x+2
=>x=1 hoặc x=5/3
5: =>\(\sqrt{x+2}\left(\sqrt{x-2}+\sqrt{x+2}\right)=0\)
=>x+2=0
=>x=-2
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Cho biểu thức: P = (sqrt(x))/(sqrt(x) + 3) + (3sqrt(x))/(x - 9) a) Rút gọn biểu thức P. với x>=0;x ne9 . b) Tim giá trị của x để P = 2 ,
a, \(P=\dfrac{\sqrt{x}}{\sqrt{x}+3}+\dfrac{3\sqrt{x}}{x-9}\)
\(\Rightarrow P=\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}+\dfrac{3\sqrt{x}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}+3\right)}\)
\(\Rightarrow P=\dfrac{x-3\sqrt{x}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}+3\right)}+\dfrac{3\sqrt{x}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}+3\right)}\)
\(\Rightarrow P=\dfrac{x-3\sqrt{x}+3\sqrt{x}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}+3\right)}\)
\(\Rightarrow P=\dfrac{x}{\left(\sqrt{x}+3\right)\left(\sqrt{x}+3\right)}\\ \Rightarrow P=\dfrac{x}{x-9}\)
b,Để P=2 \(\Leftrightarrow\dfrac{x}{x-9}=2\)
\(\Leftrightarrow x=2\left(x-9\right)\\ \Leftrightarrow x=2x-18\\ \Leftrightarrow x-18=0\\ \Leftrightarrow x=18\)
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Cho biểu thức B= (x - 2sqrt(x))/(sqrt(x) - 2) - (2x + 12sqrt(x) + 18)/(sqrt(x) + 3) với x ≥ 0 ,x ≠ 4 Rút gọn B và tìm x để B + 8 > 0 .
a: \(B=\dfrac{x-2\sqrt{x}}{\sqrt{x}-2}-\dfrac{2x+12\sqrt{x}+18}{\sqrt{x}+3}\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}-2\right)}{\sqrt{x}-2}-\dfrac{2\left(x+6\sqrt{x}+9\right)}{\sqrt{x}+3}\)
=căn x-2(căn x+3)
=-căn x-6
b: B+8>0
=>-căn x-6+8>0
=>-căn x+2>0
=>-căn x>-2
=>căn x<2
=>0<=x<4
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