Someone is asked to solve the following equation: $(x-5)/(x+1)= (x-5)/(x+3)$. This person respond "There is no solution. Cross multiply to get $(x-5)(x+3)=(x-5)(x+1)$. Divide both sides by $x-5$ and I get $x+3=x+1$. Subtracting $x$ from both sides, I get $1=3$ which is impossible. So there is no solution." Is this person right?
I mean the person is right but instead of subtracting $x$, wouldn't you subtract the constants. So I would subtract 1 on both sides and get $x+2=x$ and subtract $x$ and you get $0=2$ which is not true.