# How do you divide (x-2)^2/(x^2-5x+9)?

Jun 14, 2016

$\frac{{x}^{2} - 4 x + 4}{{x}^{2} - 5 x + 9} \text{ "=" } 1 + \frac{x - 5}{{x}^{2} - 5 x + 9}$

#### Explanation:

Look at https://socratic.org/s/avjGBRiF as a further example of the method.

Write as $\frac{\textcolor{b l u e}{{x}^{2} - 4 x + 4}}{\textcolor{g r e e n}{{x}^{2} - 5 x + 9}}$

$\text{Numerator "->" } \textcolor{b l u e}{{x}^{2} - 4 x + 4}$
$\textcolor{m a \ge n t a}{1 \times} \textcolor{g r e e n}{\left({x}^{2} - 5 x + 9\right)} \to \text{ "ul(x^2-5x+9)" "larr" Subtract}$
$\text{Remainder" ->" } 0 + \textcolor{w h i t e}{.} x - 5$

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So $\frac{{x}^{2} - 4 x + 4}{{x}^{2} - 5 x + 9} \text{ "=" } \textcolor{m a \ge n t a}{1} + \frac{x - 5}{{x}^{2} - 5 x + 9}$