1: ĐKXĐ: \(x\notin\left\{0;-5\right\}\)
2: \(P=\dfrac{x^2+2x}{2x+10}+\dfrac{x-5}{x}+\dfrac{50-5x}{2x\left(x+5\right)}\)
\(=\dfrac{x^2+2x}{2\left(x+5\right)}+\dfrac{x-5}{x}+\dfrac{50-5x}{2x\left(x+5\right)}\)
\(=\dfrac{x\left(x^2+2x\right)+2\left(x+5\right)\left(x-5\right)+50-5x}{2x\left(x+5\right)}\)
\(=\dfrac{x^3+2x^2+2x^2-50+50-5x}{2x\left(x+5\right)}\)
\(=\dfrac{x^3+4x^2-5x}{2x\left(x+5\right)}=\dfrac{x\left(x+5\right)\left(x-1\right)}{2x\left(x+5\right)}=\dfrac{x-1}{2}\)
3: \(P=\dfrac{1}{4}\)
=>\(\dfrac{x-1}{2}=\dfrac{1}{4}\)
=>\(x-1=\dfrac{1}{2}\)
=>\(x=\dfrac{3}{2}\left(nhận\right)\)
4: P<0
=>\(\dfrac{x-1}{2}< 0\)
=>x-1<0
=>x<1
Kết hợp ĐKXĐ, ta được: \(\left\{{}\begin{matrix}x< 1\\x\notin\left\{0;-5\right\}\end{matrix}\right.\)
