\(\dfrac{mx+1}{x-1}+\dfrac{x-2}{x+1}=\dfrac{\left(m+1\right).x^2-mx+2}{x^2-1}\) ĐKXĐ : \(x\ne\pm1\)
\(\Leftrightarrow\dfrac{\left(mx+1\right)-\left(x+1\right)+\left(x-2\right).\left(x-1\right)}{\left(x-1\right).\left(x+1\right)}=\dfrac{\left(m+1\right).x^2-mx+2}{x^2-1}\)
\(\Leftrightarrow\dfrac{mx^2+mx+x+1+x^2-x-2x+2}{x^2-1}=\dfrac{mx^2+x^2-mx+2}{x^2-1}\)
\(\Leftrightarrow mx^2+mx+x+1+x^2-x-2x+2=mx^2+x^2-mx+2\)
\(\Leftrightarrow mx^2+mx+x+1+x^2-x-2x+2-mx^2-x^2+mx-2=0\)
\(\Leftrightarrow2mx-2x+1=0\)
\(\Leftrightarrow\left(2m-2\right)x=-1\)
ĐK để pt có nghĩa là: \(2m-2=0\)
\(\Leftrightarrow2m=2\)
\(\Leftrightarrow m=1\)
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