Question
Reduce the following rational expression to its lowest form
$
\frac{x^2-11 x+18}{x^2-4 x+4}
$
$
\frac{x^2-11 x+18}{x^2-4 x+4}
$
✓
Answer
$\frac{x^2-11 x+18}{x^2-4 x+4}$
$\begin{aligned} & x ^2-11 x +18=( x -9)( x -2) \\ & x ^2-4 x +4=( x -2)( x -2) \\ & \frac{x^2-11 x+18}{x^2-4 x+4}=\frac{(x-9)(x-2)}{(x-2)(x-2)} \\ & =\frac{x-9}{x-2}\end{aligned}$
$\begin{aligned} & x ^2-11 x +18=( x -9)( x -2) \\ & x ^2-4 x +4=( x -2)( x -2) \\ & \frac{x^2-11 x+18}{x^2-4 x+4}=\frac{(x-9)(x-2)}{(x-2)(x-2)} \\ & =\frac{x-9}{x-2}\end{aligned}$
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