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Câu 1:
\(A=\frac{x\left(1-x^2\right)}{1+x^2}:\left[\left(\frac{\left(1-x\right)\left(x^2+x+1\right)}{1-x}+x\right)\left(\frac{\left(1+x\right)\left(x^2-x+1\right)}{1+x}+x\right)\right]\)
\(=\frac{x\left(1-x^2\right)}{x^2+1}:\left[\left(x^2+2x+1\right)\left(x^2-2x+1\right)\right]\)
\(=\frac{x\left(1-x^2\right)}{\left(1+x^2\right)\left(1+x\right)^2\left(x-1\right)^2}=\frac{x}{\left(1+x^2\right)\left(x^2-1\right)}=\frac{x}{x^4-1}\)
Câu 2: thay x vào A có :
\(A=\frac{-\frac{1}{2}}{\frac{1}{4}-1}=\frac{2}{3}\)
Câu c :
2A=1 => \(\frac{x}{x^4-1}=\frac{1}{2}\)ĐK \(\hept{\begin{cases}x\ne1\\x\ne-1\end{cases}}\)
\(\Leftrightarrow x^4-2x-1=0\Leftrightarrow\left(x+1\right)\left(x^3-x^2+x-1\right)=0\)
\(\left(x+1\right)\left(x^2+1\right)\left(x-1\right)=0\Leftrightarrow\orbr{\begin{cases}x=1\\x=-1\end{cases}}\)loại do điều kiện vậy ko có giá trị nào của x thỏa mãn
I don't now
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a) Rút gọn C
\(C=\left[\frac{x^2+3x+2}{\left(x+2\right)\left(x-1\right)}-\frac{x^2+x}{x-1}\right].\left(\frac{1}{x+1}+\frac{1}{x-1}\right)\)
\(\Rightarrow C=\left[\frac{x^2+2x+x+2}{\left(x+2\right)\left(x-1\right)}-\frac{x^2+x}{x-1}\right].\left(\frac{x-1+x+1}{\left(x+1\right)\left(x-1\right)}\right)\)
\(\Rightarrow C\left[\frac{x\left(x+2\right)+\left(x+2\right)}{\left(x+2\right)\left(x-1\right)}-\frac{x^2+x}{x-1}\right].\frac{2x}{\left(x+1\right)\left(x-1\right)}\)
\(\Rightarrow C=\left[\frac{\left(x+2\right)\left(x+1\right)}{\left(x+2\right)\left(x-1\right)}-\frac{x^2+x}{x-1}\right].\frac{2x}{\left(x+1\right)\left(x-1\right)}\)
\(\Rightarrow C=\left[\frac{x+1-x^2-x}{x-1}\right].\frac{2x}{\left(x+1\right)\left(x-1\right)}\)
\(\Rightarrow C=\left(\frac{1-x^2}{x-1}\right).\frac{2x}{\left(x+1\right)\left(x-1\right)}\)
\(\Rightarrow C=\left(\frac{-\left(x^2-1\right)}{x-1}\right).\frac{2x}{\left(x^2-1\right)}\)
\(\Rightarrow C=\frac{-2x}{x-1}\)
Vậy BT C khi rút gọn =-2x/x-1
b) Để C=2/3 Ta có:
\(\frac{-2x}{x-1}=\frac{2}{3}\)
\(\Rightarrow-2x.3=\left(x-1\right).2\)
\(\Rightarrow-6x=2x-2\)
\(\Rightarrow-6x-2x+2=0\)
\(\Rightarrow-8x+2=0\)
\(\Rightarrow-8x=-2\)
\(\Rightarrow x=\frac{-2}{-8}=\frac{1}{4}\)
Vậy x=1/4 thì C=2/3