Chapter 6 - Rational Expressions and Equations - 6.3 Addition, Subtraction, and Least Common Denominators - 6.3 Exercise Set - Page 393: 23

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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}