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a) Để M có nghĩa thì \(x\ne1;x\ne-1\)
b) \(M=\dfrac{x}{2x-2}+\dfrac{x^2-1}{2-2x^2}\)
\(=\dfrac{x^2+x}{2\left(x-1\right)\left(x+1\right)}-\dfrac{x^2-1}{2\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x+1}{2\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{1}{2x-2}\)
c) Để \(M=\dfrac{1}{2}\) thì \(\dfrac{1}{2x-2}=\dfrac{1}{2}\)
\(\Leftrightarrow2x-2=2\)
\(\Leftrightarrow x=2\)
\(a,ĐKXĐ:x-1\ne0;1-x\ne0;1+x\ne0\)
\(\Rightarrow\left[{}\begin{matrix}x\ne1\\x\ne-1\end{matrix}\right.\)
\(b,C=\dfrac{x}{2x-2}+\dfrac{x^2+1}{2-2x^2}\)
\(C=\dfrac{x^2+x}{2\left(x-1\right)\left(x+1\right)}+\dfrac{-x^2-1}{2\left(x+1\right)\left(x-1\right)}=\dfrac{1}{2x+2}\)
\(c,C=-\dfrac{1}{2}\)
\(\Rightarrow\dfrac{1}{2x+2}=-\dfrac{1}{2}\Leftrightarrow-2x-2=2\Leftrightarrow x=0\)
\(A=\left(\dfrac{x+y}{y}+\dfrac{2y}{x-y}\right)\cdot\dfrac{-\left(x-y\right)}{x^2+y^2}+\left(\dfrac{2x^2+2-2x^2+x}{2\left(2x-1\right)}\right)\cdot\dfrac{1-2x}{x+2}\)
\(=\dfrac{x^2-y^2+2y^2}{y\left(x-y\right)}\cdot\dfrac{-\left(x-y\right)}{x^2+y^2}+\dfrac{x+2}{2\left(2x-1\right)}\cdot\dfrac{-\left(2x-1\right)}{x+2}\)
\(=\dfrac{-1}{y}+\dfrac{-1}{2}=\dfrac{-2-y}{2y}\)
\(\text{a) }A=\dfrac{x}{2x+2}+\dfrac{x^2+1}{2-2x^2}\\ A=\dfrac{x}{2\left(x+1\right)}+\dfrac{x^2+1}{2\left(1-x^2\right)}\\ A=\dfrac{x}{2\left(x+1\right)}+\dfrac{x^2+1}{2\left(1-x\right)\left(1+x\right)}\\ A=\dfrac{x\left(1-x\right)}{2\left(x+1\right)\left(1-x\right)}+\dfrac{x^2+1}{2\left(x+1\right)\left(1-x\right)}\\ A=\dfrac{x-x^2+x^2+1}{2\left(x+1\right)\left(1-x\right)}\)
\(\Rightarrow\) Để \(A\) có nghĩa
\(\text{thì }\Rightarrow2\left(x+1\right)\left(1-x\right)\ne0\\ \Rightarrow\left\{{}\begin{matrix}x+1\ne0\\1-x\ne0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x\ne-1\\x\ne1\end{matrix}\right.\)
\(\text{b) }A=\dfrac{x-x^2+x^2+1}{2\left(x+1\right)\left(1-x\right)}\\ A=\dfrac{x+1}{2\left(x+1\right)\left(1-x\right)}\\ A=\dfrac{1}{2\left(1-x\right)}\\ A=\dfrac{1}{2-2x}\)
c) Để \(A=\dfrac{1}{2}\)
\(\text{thì }\Rightarrow\dfrac{1}{2-2x}=\dfrac{1}{2}\\ \Leftrightarrow2-2x=2\\ \Leftrightarrow2x=0\\ \Leftrightarrow x=0\)
Vậy......................
a: \(Q=\left(\dfrac{-x\left(x-2\right)}{2\left(x^2+4\right)}-\dfrac{2x^2}{\left(x^2+4\right)\left(x-2\right)}\right)\cdot\dfrac{2+x-x^2}{x^2}\)
\(=\dfrac{-x\left(x^2-4x+4\right)-4x^2}{2\left(x^2+4\right)\left(x-2\right)}\cdot\dfrac{-\left(x^2-x-2\right)}{x^2}\)
\(=\dfrac{-x^3+4x^2-4x-4x^2}{2\left(x^2+4\right)}\cdot\dfrac{-\left(x+1\right)}{x^2}\)
\(=\dfrac{-x\left(x^2+4\right)}{2\left(x^2+4\right)}\cdot\dfrac{-\left(x+1\right)}{x^2}=\dfrac{x+1}{x}\)
b: Để Q là số nguyên thì \(x+1⋮x\)
hay \(x=1\)
a, ĐKXĐ:\(\left\{{}\begin{matrix}2x-2\ne0\\2-2x^2\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-1\ne0\\1-x^2\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne1\\x^2\ne1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne1\\x\ne\pm1\end{matrix}\right.\Leftrightarrow x\ne\pm1\)
b, \(C=\dfrac{x}{2x-2}+\dfrac{x^2+1}{2-2x^2}\)
\(\Rightarrow C=\dfrac{x}{2\left(x-1\right)}+\dfrac{x^2+1}{2\left(1-x^2\right)}\)
\(\Rightarrow C=\dfrac{x\left(x+1\right)}{2\left(x-1\right)\left(x+1\right)}-\dfrac{x^2+1}{2\left(x-1\right)\left(x+1\right)}\)
\(\Rightarrow C=\dfrac{x^2+x-x^2-1}{2\left(x-1\right)\left(x+1\right)}\)
\(\Rightarrow C=\dfrac{x-1}{2\left(x-1\right)\left(x+1\right)}\)
\(\Rightarrow C=\dfrac{1}{2\left(x+1\right)}\)
c, \(C=\dfrac{1}{2}\)
\(\Rightarrow\dfrac{1}{2\left(x+1\right)}=\dfrac{1}{2}\\ \Rightarrow\dfrac{1}{x+1}=1\\ \Rightarrow x+1=1\\ \Rightarrow x=0\)
a: ĐKXĐ: \(x\notin\left\{1;-1\right\}\)
b: \(C=\dfrac{x}{2\left(x-1\right)}-\dfrac{x^2+1}{2\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x^2+x-x^2-1}{2\left(x-1\right)\left(x+1\right)}=\dfrac{1}{2x+2}\)
c: Để C=1/2 thì 2x+2=2
hay x=0