# Question #85911

Aug 24, 2015

If $w = i - 2$
$\textcolor{w h i t e}{\text{XXXX}} \frac{1}{5 - w} = \frac{7 + i}{50}$

#### Explanation:

$\frac{1}{5 - w}$
$\textcolor{w h i t e}{\text{XXXX}} = \frac{1}{5 - \left(i - 2\right)}$

$\textcolor{w h i t e}{\text{XXXX}} = \frac{1}{7 - i}$

To rationalize the denominator, multiply both the numerator and denominator by the conjugate of the denominator
$\textcolor{w h i t e}{\text{XXXX}} = \frac{1}{7 - i} \cdot \frac{7 + i}{7 + i}$

$\textcolor{w h i t e}{\text{XXXX}} = \frac{7 + i}{{7}^{2} - {i}^{2}} = \frac{7 + i}{49 - \left(- 1\right)} = \frac{7 + i}{50}$