a: ĐKXĐ: x∉{0;-6}
b: \(P=\frac{x^2+2x}{2x+12}+\frac{x-6}{x}+\frac{108-6x}{2x\left(x+6\right)}\)
\(=\frac{x^2+2x}{2\left(x+6\right)}+\frac{x-6}{x}+\frac{108-6x}{2x\left(x+6\right)}\)
\(=\frac{x\left(x^2+2x\right)+2\left(x-6\right)\left(x+6\right)+108-6x}{2x\left(x+6\right)}\)
\(=\frac{x^3+2x^2+2x^2-72+108-6x}{2x\left(x+6\right)}=\frac{x^3+4x^2-6x+36}{2x\left(x+6\right)}\)
\(=\frac{x^3+6x^2-2x^2-12x+6x+36}{2x\left(x+6\right)}=\frac{\left(x+6\right)\left(x^2-2x+6\right)}{2x\left(x+6\right)}\)
\(=\frac{x^2-2x+6}{2x}\)
c: \(P=\frac32\)
=>\(\frac{x^2-2x+6}{2x}=\frac32\)
=>\(x^2-2x+6=3x\)
=>\(x^2-5x+6=0\)
=>(x-2)(x-3)=0
=>x=2(nhận) hoặc x=3(nhận)
d: \(P=-\frac92\)
=>\(\frac{x^2-2x+6}{2x}=\frac{-9}{2}\)
=>\(x^2-2x+6=-9x\)
=>\(x^2+7x+6=0\)
=>(x+1)(x+6)=0
=>x=-1(nhận) hoặc x=-6(loại)
e: P=1
=>\(x^2-2x+6=2x\)
=>\(x^2-4x+6=0\)
=>\(\left(x-2\right)^2+2=0\) (vô lý)
=>x∈∅
