a: ĐKXĐ: x<>-3; x<>2
b: \(P=\frac{x+2}{x+3}-\frac{5}{x^2+x-6}+\frac{1}{2-x}\)
\(=\frac{x+2}{x+3}-\frac{5}{\left(x+3\right)\left(x-2\right)}-\frac{1}{x-2}\)
\(=\frac{\left(x+2\right)\left(x-2\right)-5-\left(x+3\right)}{\left(x-2\right)\left(x+3\right)}\)
\(=\frac{x^2-4-5-x-3}{\left(x-2\right)\left(x+3\right)}=\frac{x^2-x-12}{\left(x-2\right)\left(x+3\right)}\)
\(=\frac{\left(x-4\right)\left(x+3\right)}{\left(x-2\right)\left(x+3\right)}=\frac{x-4}{x-2}\)
c: \(P=-\frac34\)
=>\(\frac{x-4}{x-2}=\frac{-3}{4}\)
=>4(x-4)=-3(x-2)
=>4x-16=-3x+6
=>4x+3x=16+6
=>7x=22
=>\(x=\frac{22}{7}\) (nhận)
d: Để P nguyên thì x-4⋮x-2
=>x-2-2⋮x-2
=>-2⋮x-2
=>x-2∈{1;-1;2;-2}
=>x∈{3;1;4;0}
e: \(x^2-9=0\)
=>(x-3)(x+3)=0
=>x=3(nhận) hoặc x=-3(loại)
Khi x=3 thì \(P=\frac{3-4}{3-2}=\frac{-1}{1}=-1\)
