a: Khi x=1/2 thì \(B=\left(\frac12+1\right):\left(\frac12+3\right)=\frac32:\frac72=\frac37\)
b: \(A=\frac{3}{x-3}-\frac{6x}{9-x^2}+\frac{x}{x+3}\)
\(=\frac{3}{x-3}+\frac{6x}{\left(x-3\right)\left(x+3\right)}+\frac{x}{x+3}\)
\(=\frac{3\left(x+3\right)+6x+x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}=\frac{3x+9+6x+x^2-3x}{\left(x-3\right)\left(x+3\right)}\)
\(=\frac{x^2+6x+9}{\left(x-3\right)\left(x+3\right)}=\frac{\left(x+3\right)^2}{\left(x-3\right)\left(x+3\right)}=\frac{x+3}{x-3}\)
c: \(P=A\cdot B=\frac{x+3}{x-3}\cdot\frac{x+1}{x+3}=\frac{x+1}{x-3}\)
Để P là số nguyên thì x+1⋮x-3
=>x-3+4⋮x-3
=>4⋮x-3
=>x-3∈{1;-1;2;-2;4;-4}
=>x∈{4;2;5;1;7;-1}
