\(\dfrac{x-1}{x}-\dfrac{1}{x+1}=\dfrac{2x-1}{x^2+x}\)
<=>\(\dfrac{x-1}{x}-\dfrac{1}{x+1}=\dfrac{2x-1}{x\left(x+1\right)}\)
DKXD x khac 0 =>x khac 0
x+1 khac 0 x khac -1
\(\dfrac{x-1}{x}-\dfrac{1}{x+1}=\dfrac{2x-1}{x\left(x+1\right)}\)
<=>\(\dfrac{\left(x-1\right)\left(x+1\right)}{x\left(x+1\right)}-\dfrac{x}{\left(x+1\right)x}=\dfrac{2x-1}{x\left(x+1\right)}\)
<=>\(\dfrac{\left(x-1\right)\left(x+1\right)-x}{x\left(x+1\right)}=\dfrac{2x-1}{x\left(x+1\right)}\)
<=>\(\dfrac{x^2-1-x}{x\left(x+1\right)}=\dfrac{2x-1}{x\left(x+1\right)}\)
=>\(x^2-1-x=2x-1\)
<=>\(x^2-x-2x=-1+1\)
<=>\(x^2-3x=0\)
<=>x(x-3)=0
<=>x=0(loai)
x-3=0 <=> x=3(thoa man)
Vay x=3 la nghiem cua phuong trinh
