# How do you write the mixed expression (d-6)+(d+1)/(d-7) as a rational expression?

Apr 13, 2017

$\frac{{d}^{2} - 12 d + 43}{d - 7}$

#### Explanation:

We require to multiply $\left(d - 6\right) \text{ by } \frac{d - 7}{d - 7}$

$\Rightarrow \frac{\left(d - 6\right) \left(d - 7\right)}{d - 7} + \frac{d + 1}{d - 7}$

The fractions now have a $\textcolor{b l u e}{\text{common denominator}}$ so we can add the numerators while leaving the denominator as it is.

$\Rightarrow \frac{{d}^{2} - 13 d + 42 + d + 1}{d - 7}$

$= \frac{{d}^{2} - 12 d + 43}{d - 7} \leftarrow \textcolor{red}{\text{ rational expression}}$