a: \(P=\left(\dfrac{x+2}{\left(x-2\right)\left(x-3\right)}+\dfrac{x+3}{x-2}-\dfrac{x+2}{x-3}\right):\dfrac{2x+2-x}{x+1}\)
\(=\dfrac{x+2+x^2-9-x^2+4}{\left(x-3\right)\left(x-2\right)}\cdot\dfrac{x+1}{x+2}\)
\(=\dfrac{x-3}{\left(x-3\right)\left(x-2\right)}\cdot\dfrac{x+1}{x+2}=\dfrac{x+1}{x^2-4}\)
c: P=13/2
=>\(\dfrac{x+1}{x^2-4}=\dfrac{13}{2}\)
=>13x^2-52=2x+2
=>13x^2-2x-54=0
=>\(x=\dfrac{1\pm\sqrt{703}}{13}\)
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