9\(\sqrt{x}\)-9\(\sqrt{\dfrac{x}{9}}\)+x\(\sqrt{\dfrac{9}{x}}\)-x\(\sqrt{9}\) với x>0
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10 tháng 10 2020
Ta có: \(\frac{x+\sqrt{x}-6}{x-9}+\frac{x-7\sqrt{x}+19}{x+\sqrt{x}-12}-\frac{x-5\sqrt{x}}{x+4\sqrt{x}}\)
\(=\frac{x+3\sqrt{x}-2\sqrt{x}-6}{x-9}+\frac{x-7\sqrt{x}+19}{x+4\sqrt{x}-3\sqrt{x}-12}-\frac{\sqrt{x}\left(\sqrt{x}-5\right)}{\sqrt{x}\left(\sqrt{x}+4\right)}\)
\(=\frac{\sqrt{x}\left(\sqrt{x}+3\right)-2\left(\sqrt{x}+3\right)}{x-9}+\frac{x-7\sqrt{x}+19}{\sqrt{x}\left(\sqrt{x}+4\right)-3\left(\sqrt{x}+4\right)}-\frac{\sqrt{x}-5}{\sqrt{x}+4}\)
\(=\frac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}+\frac{x-7\sqrt{x}+19}{\left(\sqrt{x}+4\right)\left(\sqrt{x}-3\right)}-\frac{\left(\sqrt{x}-5\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+4\right)\left(\sqrt{x}-3\right)}\)
\(=\frac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+4\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+4\right)}+\frac{x-7\sqrt{x}+19}{\left(\sqrt{x}+4\right)\left(\sqrt{x}-3\right)}-\frac{x-8\sqrt{x}+15}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+4\right)}\)
\(=\frac{x+2\sqrt{x}-8+x-7\sqrt{x}+19-x+8\sqrt{x}-15}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+4\right)}\)
\(=\frac{x+3\sqrt{x}-4}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+4\right)}\)
\(=\frac{x+4\sqrt{x}-\sqrt{x}-4}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+4\right)}\)
\(=\frac{\sqrt{x}\left(\sqrt{x}+4\right)-\left(\sqrt{x}+4\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+4\right)}\)
\(=\frac{\left(\sqrt{x}+4\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+4\right)\left(\sqrt{x}-3\right)}\)
\(=\frac{\sqrt{x}-1}{\sqrt{x}-3}\)
10 tháng 7 2022
\(A=\left(\dfrac{3\sqrt{x}}{\sqrt{x}+3}+\dfrac{3\sqrt{x}}{x-9}\right):\dfrac{2\sqrt{x}-2-\sqrt{x}+3}{\sqrt{x}-3}\)
\(=\dfrac{3x-9\sqrt{x}+3\sqrt{x}}{x-9}\cdot\dfrac{\sqrt{x}-3}{\sqrt{x}+1}\)
\(=\dfrac{3x-6\sqrt{x}}{\sqrt{x}+3}\cdot\dfrac{1}{\sqrt{x}+1}\)
Y
26 tháng 5 2023
\(\dfrac{2\sqrt{x}}{\sqrt{x}+3}+\dfrac{x+6\sqrt{x}+9}{9-x}-\dfrac{\sqrt{x}}{\sqrt{x}+3}\left(dkxd:x\ge0,x\ne9\right)\)
\(=\dfrac{2\sqrt{x}}{\sqrt{x}+3}-\dfrac{\left(\sqrt{x}+3\right)^2}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}-\dfrac{\sqrt{x}}{\sqrt{x}+3}\)
\(=\dfrac{2\sqrt{x}\left(\sqrt{x}-3\right)-\left(x+6\sqrt{x}+9\right)-\sqrt{x}\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{2x-6\sqrt{x}-x-6\sqrt{x}-9-x+3\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{-9\sqrt{x}-9}{x-9}\) với \(x\ge0,x\ne9\)
3 tháng 3 2022
\(VT=\left(\dfrac{\sqrt{x}}{\sqrt{x}+3}+\dfrac{3}{\sqrt{x}-3}\right).\dfrac{\sqrt{x}+3}{x+9}\\ =\left(\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}+\dfrac{3\left(\sqrt{x}+3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\right).\dfrac{\sqrt{x}+3}{x+9}\\ =\dfrac{x-3\sqrt{x}+3\sqrt{x}+9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}.\dfrac{\sqrt{x}+3}{x+9}\\ =\dfrac{x+9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}.\dfrac{\sqrt{x}+3}{x+9}\\ =\dfrac{1}{\sqrt{x}-3}=VP\)
3 tháng 3 2022
\(VT=\dfrac{x-3\sqrt{x}+3\sqrt{x}+9}{x-9}\cdot\dfrac{\sqrt{x}+3}{x+9}\)
\(=\dfrac{x+9}{x+9}\cdot\dfrac{1}{\sqrt{x}-3}=\dfrac{1}{\sqrt{x}-3}=VP\)
7 tháng 10 2023
a) \(\dfrac{\sqrt{x}}{\sqrt{x}+3}+\dfrac{2\sqrt{x}}{\sqrt{x}-3}-\dfrac{3x+9}{x-9}\left(x\ge0;x\ne0\right)\)
\(=\dfrac{\sqrt{x}.\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+3\right).\left(\sqrt{x-3}\right)}+\dfrac{2\sqrt{x}.\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-3\right).\left(\sqrt{x}+3\right)}-\dfrac{3x+9}{\left(\sqrt{x}-3\right).\left(\sqrt{x+3}\right)}\)
\(=\dfrac{x-3\sqrt{x}+2x+6\sqrt{x}-3x-9}{\left(\sqrt{x}+3\right).\left(\sqrt{x-3}\right)}\)
\(=\dfrac{3\sqrt{x}-9}{\left(\sqrt{x}+3\right).\left(\sqrt{x}-3\right)}\)
\(=\dfrac{3.\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+3\right).\left(\sqrt{x}-3\right)}\)
\(=\dfrac{3}{\sqrt{x}+3}\)
7 tháng 10 2023
b) \(\dfrac{3}{\sqrt{x}-1}-\dfrac{\sqrt{x}+5}{x-1}\left(x\ge0;x\ne1\right)\)
\(=\dfrac{3.\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right).\left(\sqrt{x}+1\right)}-\dfrac{\sqrt{x}+5}{\left(\sqrt{x}-1\right).\left(\sqrt{x}+1\right)}\)
\(=\dfrac{3\sqrt{x}+3-\sqrt{x}-5}{\left(\sqrt{x}-1\right).\left(\sqrt{x}+1\right)}\)
\(=\dfrac{2\sqrt{x}-2}{\left(\sqrt{x}-1\right).\left(\sqrt{x}+1\right)}\)
\(=\dfrac{2.\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right).\left(\sqrt{x}+1\right)}\)
\(=\dfrac{2}{\sqrt{x}+1}\)
12 tháng 12 2022
a: \(=\dfrac{x-3\sqrt{x}-x-9}{x-9}:\dfrac{3\sqrt{x}+1-\sqrt{x}+3}{\sqrt{x}\left(\sqrt{x}-3\right)}\)
\(=\dfrac{-3\left(\sqrt{x}+3\right)}{x-9}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)}{2\sqrt{x}+4}=\dfrac{-3\sqrt{x}}{2\sqrt{x}+4}\)
b: Để A>-1 thì A+1>0
=>\(-3\sqrt{x}+2\sqrt{x}+4>0\)
=>-căn x>-4
=>0<x<16
24 tháng 7 2018
Ta có :
a , \(M=2\left(\dfrac{\sqrt{x}}{\sqrt{x}+3}-\dfrac{x+9}{x-9}\right):\left[\dfrac{3\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-3\right)}-\dfrac{\sqrt{x}-3}{\sqrt{x}\left(\sqrt{x}-3\right)}\right]\)
\(M=\left[\dfrac{2\sqrt{x}\left(\sqrt{x}-3\right)}{x-9}-\dfrac{2\left(x+9\right)}{x-9}\right]:\left[\dfrac{3\sqrt{x}+1-\sqrt{x}+3}{\sqrt{x}\left(\sqrt{x}-3\right)}\right]\)
\(M=\left(\dfrac{2x-6\sqrt{x}-2x-18}{x-9}\right).\left[\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)}{2\sqrt{x}+4}\right]\)
\(M=\dfrac{-6\sqrt{x}\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(2\sqrt{x}+4\right)}\)
\(M=\dfrac{-6\sqrt{x}}{2\left(\sqrt{x}+2\right)}\)
\(M=-\dfrac{3\sqrt{x}}{\sqrt{x}+2}\)
b , mik ko chắc chắn nên mik chưa làm nhé !
14 tháng 8 2023
Sửa đề: \(\dfrac{\sqrt{x}}{\sqrt{x}+3}+\dfrac{2\sqrt{x}}{\sqrt{x}-3}-\dfrac{3x+9}{x-9}\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)+2\sqrt{x}\left(\sqrt{x}+3\right)-3x-9}{x-9}\)
\(=\dfrac{x+3\sqrt{x}+2x+6\sqrt{x}-3x-9}{x-9}\)
\(=\dfrac{9\sqrt{x}-9}{x-9}\)
PL
4 tháng 1 2023
Với x ≥ 0; x ≠ 9 ta có:
\(A=\dfrac{\sqrt{x}}{\sqrt{x}+3}+\dfrac{2\sqrt{x}}{\sqrt{x}-3}-\dfrac{3x+9}{x-9}\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x-3}\right)+2\sqrt{x}\left(\sqrt{x}+3\right)-3x-9}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{x-3\sqrt{x}+2x+6\sqrt{x}-3x-9}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{3\sqrt{x}-9}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{3\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{3}{\sqrt{x}+3}\)
Vậy \(A=\dfrac{3}{\sqrt{x}+3}\).
\(=9\sqrt{x}-9.\dfrac{1}{3}.\sqrt{x}+x.\dfrac{1}{\sqrt{x}}.\sqrt{9}-3x\)
\(=9\sqrt{x}-3\sqrt{x}+3\sqrt{x}-3x\)
\(=-3x+9\sqrt{x}\)
\(=9\sqrt{x}-9\cdot\dfrac{1}{3}\sqrt{x}+3\sqrt{\dfrac{x^2}{x}}-x\sqrt{9}\\ =9\sqrt{x}-3\sqrt{x}+3\sqrt{x}-3x\\ =9\sqrt{x}-3x=3\sqrt{x}\left(3\sqrt{x}-1\right)\)