#### Answer

$0$

#### Work Step by Step

Adding the numerators and copying the denominator, the given expression, $
\dfrac{t^2-5t}{t-1}+\dfrac{5t-t^2}{t-1}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{t^2-5t+5t-t^2}{t-1}
\\\\=
\dfrac{0}{t-1}
\\\\=
0
.\end{array}