Appendix A - Review - A.6 Rational Expressions - A.6 Assess Your Understanding - Page A53: 44

$\dfrac{x+6}{x-1} , \quad x\neq 1$

The denominators are additive inverses of each other so we factor out factoring $-1$ out of the denominator of the second rational as follows: \begin{align*} \frac{6}{x-1}-\frac{x}{1-x}&=\frac{6}{x-1}-\frac{x}{-(x-1)}\\ \\&=\frac{6}{x-1}-\frac{-x}{x-1}\\ \\&=\frac{6}{x-1}+\frac{x}{x-1}\\ \\&=\frac{x+6}{x-1}, \quad x\ne1\end{align*}