# How do you add or subtract (t^2 + 6t)/(t-1) – (7)/(t – 1)?

May 27, 2015

Assuming $t \ne 1$

$\frac{{t}^{2} + 6 t}{t - 1} - \frac{7}{t - 1}$

Since both terms have a common denominator the expression can be re-written as
$\frac{{t}^{2} + 6 t - 7}{t - 1}$

Factoring the numerator:
$= \frac{\left(t - 1\right) \left(t + 7\right)}{t - 1}$

$= t + 7$