1. \(\frac{x+3}{x+1}+\frac{x-2}{x}=2\) DKXD : \(x\ne-1;x\ne0\)
↔ \(\frac{x\left(x+3\right)}{x\left(x+1\right)}+\frac{\left(x-2\right)\left(x+1\right)}{x\left(x+1\right)}=\frac{2x\left(x+1\right)}{x\left(x+1\right)}\)
→ \(x\left(x+3\right)+\left(x-2\right)\left(x+1\right)=2x\left(x+1\right)\)
↔ \(x^2+3x+x^2+x-2x-2=2x^2+2x\)
↔ \(x^2+3x+x^2+x-2x-2x^2-2x=2\)
↔ \(0x=2\)
Ptr vo nghiem
2.\(\frac{2x-3}{x-2}=\frac{2x+1}{x}\) DKXD : \(x\ne0;x\ne2\)
↔ \(\frac{x\left(2x-3\right)}{x\left(x-2\right)}=\frac{\left(2x+1\right)\left(x-2\right)}{x\left(x-2\right)}\)
→ \(x\left(2x-3\right)=\left(2x+1\right)\left(x-2\right)\)
↔ \(2x^2-3x=2x^2-4x+x-2\)
↔ \(2x^2-3x-2x^2+4x-x=-2\)
↔ \(0x=-2\)
Ptr vo nhiem
