\(\dfrac{y-1}{m-1}-\dfrac{2m^2\left(y-1\right)}{m^4-1}-\dfrac{y-1}{m+1}=\dfrac{2y-2+1}{1-m^4}=\dfrac{2\left(y-1\right)}{1-m^4}+\dfrac{1}{1-m^4}\)
\(\Leftrightarrow\dfrac{y-1}{m-1}-\dfrac{2m^2\left(y-1\right)}{m^4-1}-\dfrac{y-1}{m+1}+\dfrac{2\left(y-1\right)}{m^4-1}=\dfrac{1}{1-m^4}\)
\(\Leftrightarrow\left(y-1\right)\left(\dfrac{1}{m-1}-\dfrac{2m^2}{m^4-1}-\dfrac{1}{m+1}+\dfrac{2}{m^4-1}\right)=\dfrac{1}{1-m^4}\)
\(\Leftrightarrow\left(y-1\right)\left(\dfrac{2}{m^2-1}-\dfrac{2\left(m^2-1\right)}{m^4-1}\right)=\dfrac{1}{1-m^4}\)
\(\Leftrightarrow\left(y-1\right)\left(\dfrac{2}{m^2-1}-\dfrac{2\left(m^2-1\right)}{\left(m^2-1\right)\left(m^2+1\right)}\right)=\dfrac{1}{1-m^4}\)
\(\Leftrightarrow\left(y-1\right)\left(\dfrac{2}{m^2-1}-\dfrac{2}{m^2+1}\right)=\dfrac{1}{1-m^4}\)
\(\Leftrightarrow\left(y-1\right)\left(\dfrac{4}{m^4-1}\right)=\dfrac{-1}{m^4-1}\)
\(\Leftrightarrow y-1=-\dfrac{1}{4}\)
\(\Leftrightarrow y=1-\dfrac{1}{4}=\dfrac{3}{4}\)
