a:
ĐKXĐ: \(x\notin\left\{3;-3\right\}\)
\(P=\dfrac{x^2-6x+9}{9-x^2}+\dfrac{8+4x}{x+3}\)
\(=\dfrac{\left(x-3\right)^2}{-\left(x-3\right)\left(x+3\right)}+\dfrac{4x+8}{x+3}\)
\(=\dfrac{-x+3}{x+3}+\dfrac{4x+8}{x+3}=\dfrac{-x+3+4x+8}{x+3}\)
\(=\dfrac{3x+11}{x+3}\)
b: Để P nguyên thì \(3x+11⋮x+3\)
=>\(3x+9+2⋮x+3\)
=>\(2⋮x+3\)
=>\(x+3\in\left\{1;-1;2;-2\right\}\)
=>\(x\in\left\{-2;-4;-1;-5\right\}\)
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