Answer
$\dfrac{12}{x-1}$
Work Step by Step
The expression $
\dfrac{7}{x-1}+\dfrac{10x}{x^2-1}-\dfrac{5}{x+1}
$ simplifies to
\begin{array}{l}
\dfrac{7}{x-1}+\dfrac{10x}{(x+1)(x-1)}-\dfrac{5}{x+1}
\\\\=
\dfrac{(x+1)(7)+10x(1)-5(x-1)}{(x+1)(x-1)}
\\\\=
\dfrac{7x+7+10x-5x+5}{(x+1)(x-1)}
\\\\=
\dfrac{(7x+10x-5x)+(7+5)}{(x+1)(x-1)}
\\\\=
\dfrac{12x+12}{(x+1)(x-1)}
\\\\=
\dfrac{12(x+1)}{(x+1)(x-1)}
\text{... cancel $(x+1)$}
\\\\=
\dfrac{12}{x-1}
.\end{array}
