Answer
$P=(2x+3)
\text{ }
$
Work Step by Step
Adding all the sides of the given quadrilateral, then the perimeter is
\begin{array}{l}\require{cancel}
P=\dfrac{5}{x-1}+\dfrac{3x}{x-1}+\dfrac{x^2-8}{x-1}+\dfrac{x^2-2x}{x-1}
\\\\
P=\dfrac{5+3x+x^2-8+x^2-2x}{x-1}
\\\\
P=\dfrac{(x^2+x^2)+(3x-2x)+(5-8)}{x-1}
\\\\
P=\dfrac{2x^2+x-3}{x-1}
\\\\
P=\dfrac{(2x+3)(x-1)}{x-1}
\\\\
P=\dfrac{(2x+3)(\cancel{x-1})}{\cancel{x-1}}
\\\\
P=(2x+3)
\text{ }
.\end{array}
