Question

[super xity]

cho C= (x/x+1   + 1/x-1   - 2x/1-x^2 ): x+1/6

a, Tìm x để C=x

giải giùm nha mik tick cho

Answer 1

[Hoàng Lê Bảo Ngọc]

\(C=\left(\frac{x}{x+1}+\frac{1}{x-1}-\frac{2x}{1-x^2}\right):\left(\frac{x+1}{6}\right)\) (ĐK : x khác 1 và x khác -1)

\(=\frac{x\left(x-1\right)+x+1+2x}{\left(x-1\right)\left(x+1\right)}.\frac{6}{x+1}=\frac{x^2+2x+1}{\left(x-1\right)\left(x+1\right)}.\frac{6}{x+1}=\frac{6.\left(x+1\right)^2}{\left(x+1\right)^2\left(x-1\right)}=\frac{6}{x-1}\)

Để C = x tức là \(\frac{6}{x-1}=x\Leftrightarrow x^2-x-6=0\Leftrightarrow\left(x+2\right)\left(x-3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=3\\x=-2\end{cases}}\)