\(\dfrac{M}{N}=\dfrac{x^3-4x^2-3x+18}{x^3-2x^2-15x+36}\)
\(=\dfrac{x^3-3x^2-x^2+3x-6x+18}{x^3-3x^2+x^2-3x-12x+36}\)
\(=\dfrac{\left(x-3\right)\left(x^2-x-6\right)}{\left(x-3\right)\left(x^2+x-12\right)}=\dfrac{\left(x-3\right)\left(x+2\right)}{\left(x+4\right)\left(x-3\right)}=\dfrac{x+2}{x+4}\)
Để P nguyên thì x+4-2 chia hết cho x+4
=>\(x+4\in\left\{1;-1;2;-2\right\}\)
=>\(x\in\left\{-3;-5;-2;-6\right\}\)
=>a=-2; b=-6
=>a*b=12
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