ko biết

c/đễ A<0  <=>  -1/X-2 <0  <=> x-2<0  <=>x<2 

a)  \(A=\left(\frac{x}{x^2-4}+\frac{2}{2-x}+\frac{1}{x+2}\right):\left(x-2+\frac{10-x^2}{x+2}\right)\)

\(ĐKXĐ:x\ne\pm2\)

\(A=\left(\frac{x}{x^2-4}-\frac{2}{x-2}+\frac{1}{x+2}\right):\left(\frac{x^2-4}{x+2}+\frac{10-x^2}{x+2}\right)\)

\(A=\left(\frac{x}{x^2-4}-\frac{2\left(x+2\right)}{x^2-4}+\frac{x-2}{x^2-4}\right):\frac{6}{x+2}\)

\(A=\frac{x-2\left(x+2\right)+x-2}{x^2-4}:\frac{6}{x+2}\)

\(A=\frac{-6}{x^2-4}:\frac{6}{x+2}\)

\(A=\frac{-6}{\left(x-2\right)\left(x+2\right)}\times\frac{x+2}{6}\)

\(A=\frac{-1}{x-2}\)

b) Ta có \(\left|x\right|=\frac{1}{2}\Leftrightarrow x=\pm\frac{1}{2}\)

TH1: Nếu \(x=\frac{1}{2}\)thì:

\(A=\frac{-1}{\frac{1}{2}-2}=\frac{-1}{\frac{-3}{2}}=-1\times\frac{2}{-3}=\frac{2}{3}\)

TH2: nếu \(x=\frac{-1}{2}\)thì:

\(A=\frac{-1}{\frac{-1}{2}-2}=\frac{-1}{\frac{-5}{2}}=-1\times\frac{2}{-5}=\frac{2}{5}\)

Vậy tại \(\left|x\right|=\frac{1}{2}\)thì \(A=\left\{\frac{2}{3};\frac{2}{5}\right\}\)

c) Để \(A< 0\)thì \(\frac{-1}{x-2}< 0\)

\(\Leftrightarrow x-2>0\)

\(\Leftrightarrow x>2\)

Vậy để \(A< 0\)thì \(x>2\)

tổng 2 số là 150, tổng của 1/6 số này và 1/9 số kia = 18. Tìm 2 số đó

\(\left(x^2-\frac{1}{x^2}\right):\left(x^2+\frac{1}{x^2}\right)=a\Leftrightarrow\left(x^4-1\right):\left(x^4+1\right)=a\Leftrightarrow x^4=\frac{1+a}{1-a}\)

\(M=\left(\frac{1+a}{1-a}-\frac{1-a}{1+a}\right):\left(\frac{1+a}{1-a}+\frac{1-a}{1+a}\right)=\frac{2a}{1+a^2}\)

Ta có: \(\left(x^2-\frac{1}{x^2}\right):\left(x^2+\frac{1}{x^2}\right)=a=>\left(\frac{x^4-1}{x^2}\right):\left(\frac{x^4+1}{x^2}\right)=a\)

\(=>\frac{x^4-1}{x^2}.\frac{x^2}{x^4+1}=a=>\frac{x^4-1}{x^4+1}=a=>x^4-1=a\left(x^4+1\right)=ax^4+a\)

\(=>x^4-ax^4=a+1=>x^4=\frac{a+1}{1-a}\)

Thay vào M,ta có:

\(M=\left(x^4-\frac{1}{x^4}\right):\left(x^4+\frac{1}{x^4}\right)=\left(\frac{a+1}{1-a}-\frac{1}{\frac{a+1}{1-a}}\right):\left(\frac{a+1}{1-a}+\frac{1}{\frac{a+1}{1-a}}\right)\)

\(=\left(\frac{a+1}{1-a}-\frac{1-a}{a+1}\right):\left(\frac{a+1}{1-a}+\frac{1-a}{a+1}\right)=\frac{\left(a+1\right)^2-\left(1-a\right)^2}{\left(1-a\right)\left(a+1\right)}:\frac{\left(a+1\right)^2+\left(1-a\right)^2}{\left(1-a\right)\left(a+1\right)}\)

\(=\frac{\left(a+1\right)^2-\left(1-a\right)^2}{\left(1-a\right)\left(a+1\right)}.\frac{\left(1-a\right)\left(a+1\right)}{\left(a+1\right)^2+\left(1-a\right)^2}=\frac{\left(a+1\right)^2-\left(1-a\right)^2}{\left(a+1\right)^2+\left(1-a\right)^2}\)

\(=\frac{a^2+2a+1-\left(1-2a+a^2\right)}{a^2+2a+1+1-2a+a^2}=\frac{a^2+2a+1-1+2a-a^2}{a^2+2a+1+1-2a+a^2}=\frac{4a}{2a^2+2}=\frac{2.2a}{2.\left(a^2+1\right)}=\frac{2a}{a^2+1}\)

Vậy \(M=\frac{2a}{a^2+1}\)

Làm hộ mk, phân tích đa thức thành nhân tử

a^4   b^4   c^4 - 2*a^2*b^2 - 2*b^2*c^2 - 2*c^2*a^2

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Bài 2:

\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).......\left(1-\frac{1}{2004}\right)\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{2003}{2004}\)

\(=\frac{1}{2004}\)

Bài 2

=1/2 x 2/3 ... x 2003/2004

=1/2004

2.

1/2004

sudy well

study well

ĐK: \(x\ne\pm2\)

\( a)A = \left( {\dfrac{3}{{2x + 4}} + \dfrac{x}{{2 - x}} + \dfrac{{2{x^2} + 3}}{{{x^2} - 4}}} \right):\left( {\dfrac{{2x - 1}}{{4x - 8}}} \right)\\ = \dfrac{{3\left( {2 - x} \right) + 2x\left( {2 + x} \right) - 4{x^2} - 6}}{{2\left( {x + 2} \right)\left( {x - 2} \right)}}:\dfrac{{2x - 1}}{{4\left( {x - 2} \right)}}\\ = \dfrac{{ - 2{x^2} + x}}{{2\left( {x + 2} \right)}}.\dfrac{{4\left( {x - 2} \right)}}{{2x - 1}} = \dfrac{{2x}}{{x + 2}} \)

\(b)\dfrac{{2x}}{{x + 2}} - 2 = \dfrac{{2x - 2x + 4}}{{x + 2}} = \dfrac{4}{{x + 2}}\)

Ta có: \(4>0\) để \(\dfrac{4}{{x + 2}} < 0 \Rightarrow x + 2 < 0 \Rightarrow x < - 2\)

\(c)\left| {x - 1} \right| = 3 \Leftrightarrow \left[ \begin{array}{l} x - 1 = 3\\ x - 1 = - 3 \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} x = 4\left( {tm} \right)\\ x = - 2\left( {ktm} \right) \end{array} \right.\)

Với \(x = 4 \Rightarrow A = \dfrac{{2.4}}{{4 + 2}} = \dfrac{4}{3}\)

\( d)\left| A \right| = \left| {\dfrac{{2x}}{{x + 2}}} \right| = 1\\ T{H_1}:\dfrac{{2x}}{{x + 2}} = 1 \Leftrightarrow 2x = x + 2 \Leftrightarrow x = 2\\ T{H_2}:\dfrac{{2x}}{{x + 2}} = - 1 \Leftrightarrow 2x = - x - 2 \Leftrightarrow x = - \dfrac{2}{3} \)