How many real solutions does x+2/x-3 = 4/x-3 + 1 have?

Multiply every term by $x-3$, noting that $x\ne3$: $x+2=4+(x-3)$. The right side simplifies to $x+1$, so the equation becomes $x+2=x+1$, which reduces to $2=1$. That is never true, so there are no real solutions, choice F. Choice G assumes the equation still yields exactly one value, but the variable terms cancel and leave a contradiction. Choice H assumes a quadratic, which this is not, since the $x$ terms cancel. Choice J would require a true statement like $0=0$, but here the result $2=1$ is false for every $x$.