rút gon B=2/√x+1+√x-15/25-x
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Bài 1 (2,0 điểm) Cho ,A= sqrt x -2 sqrt x+1 ,B- x x-4 + 1 sqrt x-2 + 1 sqrt x+2 ,DK:x>=0,x ne4 a) Tính giá trị của A hix = 25 b) Rút gon B: c) Tim giá trị nhỏ nhất của biểu thức: P= Lambda.B
a: \(A=\sqrt{x-2\sqrt{x}+1}=\left|\sqrt{x}-1\right|\)
Khi x=25 thì A=|5-1|=4
b: \(B=\dfrac{-x+\sqrt{x}+2+\sqrt{x}-2}{x-4}=\dfrac{-x+2\sqrt{x}}{x-4}=\dfrac{-\sqrt{x}}{\sqrt{x}+2}\)
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Cho biểu thức M (x/x2 - 25 - x-5/x2 + 5x) : 2x-5/x2+ x
a) rút gon biểu thức M
b) Tính giá trị của M khi x = 2,5
c) Tìm x để M = 1
e) Tìm x thuộc Z để M thuộc Z
Cho biểu thức A=\(\frac{1}{15}.\frac{225}{x+2}+\frac{3}{14}+\frac{196}{3x+6}\left(x\in Z;x\ne2\right)\)
a) rút gon A
b) tìm x thuộc Z để Acó giá trị nguyên
cho xyz=2 rút gon B=x/xy+x+2+y/yz+y+1+2z/xz+2z+2
Rút gon: 1/x+1+1/(x+1)(x+2)+...+1/(x+2016)(x+2017)
= 1/x+1 + 1/x+1 - 1/x+2 + 1/x+2 - 1/x+3 + .... + 1/x+2016 - 1/x+2017
= 2/x+1 - 1/x+2017
k mk nha
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Rút gon biểu thức
\(\dfrac{x}{x-4}+\dfrac{1}{\sqrt{x}+2}-\dfrac{1}{2-\sqrt{x}}\)
\(=\dfrac{x+\sqrt{x}-2+\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{x+2\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{\sqrt{x}}{\sqrt{x}-2}\)
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Bài 1: Rút gon
a) B=\(\left(\dfrac{x}{3x-9}+\dfrac{2x-3}{3x-x^2}\right).\dfrac{3x^2-9x}{x^2+6x+9}\)
b) A=\(\left(\dfrac{x}{x^2-4}+\dfrac{2}{2-x}+\dfrac{1}{x+2}\right):\dfrac{1}{x+2}\)
a) Ta có: \(B=\left(\dfrac{x}{3x-9}+\dfrac{2x-3}{3x-x^2}\right)\cdot\dfrac{3x^2-9x}{x^2+6x+9}\)
\(=\left(\dfrac{x}{3\left(x-3\right)}-\dfrac{2x-3}{x\left(x-3\right)}\right)\cdot\dfrac{3x\left(x-3\right)}{\left(x+3\right)^2}\)
\(=\left(\dfrac{x^2}{3x\left(x-3\right)}-\dfrac{3\left(2x-3\right)}{3x\left(x-3\right)}\right)\cdot\dfrac{3x\left(x-3\right)}{\left(x+3\right)^2}\)
\(=\dfrac{x^2-6x+9}{3x\left(x-3\right)}\cdot\dfrac{3x\left(x-3\right)}{\left(x+3\right)^2}\)
\(=\dfrac{x^2-6x+9}{x^2+6x+9}\)
b) Ta có: \(A=\left(\dfrac{x}{x^2-4}+\dfrac{2}{2-x}+\dfrac{1}{x+2}\right):\dfrac{1}{x+2}\)
\(=\left(\dfrac{x}{\left(x-2\right)\left(x+2\right)}-\dfrac{2}{x-2}+\dfrac{1}{x+2}\right):\dfrac{1}{x+2}\)
\(=\left(\dfrac{x}{\left(x-2\right)\left(x+2\right)}-\dfrac{2\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\dfrac{x-2}{\left(x+2\right)\left(x-2\right)}\right):\dfrac{1}{x+2}\)
\(=\left(\dfrac{x-2x-4+x-2}{\left(x-2\right)\left(x+2\right)}\right):\dfrac{1}{x+2}\)
\(=\dfrac{-6}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x+2}{1}\)
\(=\dfrac{-6}{x-2}\)
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Cho biểu thức: G= (x-\(\sqrt{x}\)+2/x-1 -1/\(\sqrt{x}\)-1)* x+2\(\sqrt{x}\)+1/2x-2\(\sqrt{x}\) ( với x>0; x≠1)
rút gon G
Ta có: \(G=\left(\dfrac{x-\sqrt{x}+2}{x-1}-\dfrac{1}{\sqrt{x}-1}\right)\cdot\dfrac{x+2\sqrt{x}+1}{2x-2\sqrt{x}}\)
\(=\dfrac{x-\sqrt{x}+2-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\cdot\dfrac{\left(\sqrt{x}+1\right)^2}{2\sqrt{x}\left(\sqrt{x}-1\right)}\)
\(=\dfrac{\left(\sqrt{x}-1\right)^2\cdot\left(\sqrt{x}+1\right)^2}{2\sqrt{x}\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)^2}\)
\(=\dfrac{\sqrt{x}+1}{2\sqrt{x}}\)
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Rút gon phân thức B=2+x/x-2 -4x2/x2-4 – 2-x/2+x
ta có B=2+\(\frac{x}{x-2}\)- \(\frac{4x^2}{x^2-4}\)- \(\frac{2-x}{x+2}\)
=\(\frac{2\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}-\frac{4x^2}{\left(x-2\right)\left(x+2\right)}-\frac{\left(x-2\right)\left(2-x\right)}{\left(x-2\right)\left(x+2\right)}\)
=\(\frac{2\left(x-2\right)\left(x+2\right)+x\left(x+2\right)-4x^2-\left(x-2\right)\left(2-x\right)}{\left(x-2\right)\left(x+2\right)}\)
=\(\frac{\left(x+2\right)\left\{2\left(x-2\right)+x\right\}-\left\{4x^2-\left(x-2\right)^2\right\}}{\left(x-2\right)\left(x+2\right)}=\frac{\left(x+2\right)\left(3x-4\right)-\left(2x-x+2\right)\left(2x+x-2\right)}{\left(x-2\right)\left(x+2\right)}\)
=\(\frac{\left(x+2\right)\left(3x-4\right)-\left(x+2\right)\left(3x-2\right)}{\left(x-2\right)\left(x+2\right)}\)=\(\frac{\left(x+2\right)\left(3x-4-3x+2\right)}{\left(x-2\right)\left(x+2\right)}\)
=\(\frac{-2\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\)=\(\frac{-2}{x-2}\)
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