a: \(A=\dfrac{x+15}{x^2-9}+\dfrac{2}{x+3}\)
\(=\dfrac{x+15}{\left(x-3\right)\left(x+3\right)}+\dfrac{2}{x+3}\)
\(=\dfrac{x+15+2\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{x+15+2x-6}{\left(x-3\right)\left(x+3\right)}=\dfrac{3x+9}{\left(x-3\right)\left(x+3\right)}=\dfrac{3}{x-3}\)
b: \(A=-\dfrac{1}{2}\)
=>\(\dfrac{3}{x-3}=-\dfrac{1}{2}\)
=>\(x-3=3\cdot\left(-2\right)=-6\)
=>x=-6+3=-3(loại)
c: Để A nguyên thì \(x-3\inƯ\left(3\right)\)
=>\(x-3\in\left\{1;-1;3;-3\right\}\)
=>\(x\in\left\{4;2;6;0\right\}\)
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