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Sagot :
Consider the given expression,
[tex]\frac{3}{x+1}-\frac{1}{x-1}-\frac{2x}{x^2-1}[/tex]Consider the algebraic identity,
[tex]a^2-b^2=(a+b)(a-b)[/tex]Simplify the expression as,
[tex]\begin{gathered} \frac{3}{x+1}-\frac{1}{x-1}-\frac{2x}{(x-1)(x+1)} \\ \frac{3(x-1)-1(x+1)-2x(1)}{(x-1)(x+1)} \\ \frac{3x-3-x-1-2x}{(x-1)(x+1)} \\ \frac{-4}{(x-1)(x+1)} \\ \frac{-4}{x^2-1} \end{gathered}[/tex]Thus, the given expression is in simplified form gives,
[tex]\frac{3}{x+1}-\frac{1}{x-1}-\frac{2x}{x^2-1}=\frac{-4}{x^2-1}[/tex]
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