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\(\frac{4x}{x^2-1}-\frac{x+1}{x-1}\)
\(=\frac{4x-(x+1)^2}{x^2-1}\)
\(=\frac{4x-(x^2+2x+1)}{x^2-1}\)
\(=\frac{-(x^2+2x+1-4x)}{x^2-1}\)
\(=-\frac{x^2-2x+1}{x^2-1}\)
\(=-\frac{(x-1)^2}{x^2-1}\)
\(=\frac{(x-1)^2}{1-x^2}\)
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