\(P=\dfrac{2x-9}{\left(x-2\right)\left(x-3\right)}-\dfrac{x+3}{x-2}+\dfrac{2x+1}{x-3}\)
\(=\dfrac{2x-9}{\left(x-2\right)\left(x-3\right)}-\dfrac{\left(x+3\right)\left(x-3\right)}{\left(x-2\right)\left(x-3\right)}+\dfrac{\left(2x+1\right)\left(x-2\right)}{\left(x-2\right)\left(x-3\right)}\)
\(=\dfrac{2x-9-\left(x^2-9\right)+2x^2-3x-2}{\left(x-2\right)\left(x-3\right)}\)
\(=\dfrac{x^2-x-2}{\left(x-2\right)\left(x-3\right)}=\dfrac{\left(x+1\right)\left(x-2\right)}{\left(x-2\right)\left(x-3\right)}\)
\(=\dfrac{x+1}{x-3}\)
b.
\(x=5\Rightarrow P=\dfrac{5+1}{5-3}=3\)
c.
\(P=\dfrac{x+1}{x-3}=\dfrac{x-3+4}{x-3}=1+\dfrac{4}{x-3}\)
\(P\in Z\Rightarrow\dfrac{4}{x-3}\in Z\Rightarrow x-3=Ư\left(4\right)\)
\(\Rightarrow x-3=\left\{-4;-2;-1;1;2;4\right\}\)
\(\Rightarrow x=\left\{-1;1;2;4;5;7\right\}\)
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