Điều kiện xác định:
\(x\ne0;x+5\ne0\)
<=>\(x\ne0;x\ne-5\)
\(P=\frac{x^2+2x}{2x+10}+\frac{x-5}{x}+\frac{50-5x}{2x\left(x+5\right)}\)
\(=\frac{x^2+2x}{2\left(x+5\right)}+\frac{x-5}{x}+\frac{50-5x}{2x\left(x+5\right)}\)
=\(\frac{x\left(x^2+2x\right)}{2x\left(x+5\right)}+\frac{2\left(x+5\right)\left(x-5\right)}{2x\left(x+5\right)}+\frac{50-5x}{2x\left(x+5\right)}\)
\(=\frac{x^3+2x^2}{2x\left(x+5\right)}+\frac{2x^2-50}{2x\left(x+5\right)}+\frac{50-5x}{2x\left(x+5\right)}\)
=\(\frac{x^3+2x^2+2x^2-50+50-5x}{2x\left(x+5\right)}=\frac{x^3+4x^2-5x}{2x\left(x+5\right)}\)
\(=\frac{x\left(x^2+4x-5\right)}{2x\left(x+5\right)}=\frac{x\left(x^2-x+5x-5\right)}{2x\left(x+5\right)}\)
\(\frac{x\left[x\left(x-1\right)+5\left(x-1\right)\right]}{2x\left(x+5\right)}=\frac{x\left(x-1\right)\left(x+5\right)}{2x\left(x+5\right)}=\frac{x-1}{2}\)
*Với P=1 thì \(\frac{x-1}{2}\)=1
<=>x-1=2
<=>x=3
*Với P= -3 thì \(\frac{x-1}{2}=-3\)
<=>x-1 = -6
<=>x=-5
Mà x\(\ne\)5
nên với P=-3 thì không tìm được x
với P = 1 thì x=3