a.
Khi \(x=-5\Rightarrow B=\dfrac{2.\left(-5\right)-2}{5}=-\dfrac{12}{5}\)
b.
\(A=\dfrac{2x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\dfrac{x-3}{\left(x-3\right)\left(x+3\right)}-\dfrac{2x^2-12}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{2x\left(x+3\right)-\left(x-3\right)-\left(2x^2-12\right)}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{5x+15}{\left(x-3\right)\left(x+3\right)}=\dfrac{5\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{5}{x-3}\)
c.
\(M=AB=\dfrac{5}{x-3}.\dfrac{2x-2}{5}=\dfrac{2x-2}{x-3}=\dfrac{2\left(x-3\right)+4}{x-3}=2+\dfrac{4}{x-3}\)
Để M nguyên \(\Rightarrow\dfrac{4}{x-3}\) nguyên \(\Rightarrow x-3=Ư\left(4\right)\)
\(\Rightarrow x-3=\left\{-4;-2;-1;1;2;4\right\}\)
\(\Rightarrow x=\left\{-1;1;2;4;5;7\right\}\)
