Relation of x and c

$\dfrac{x+c}{x+1}=c+1$ , multiplying both sides by $x+1$ , we get

$x+c=(c+1)(x+1)$ , expanding the right side, we get

$x+c=cx+c+x+1$ , simplifying, we get

$0=cx+1$ , finally, further simplifying, we get

$\large \boxed{x=-\dfrac{1}{c}}$

Basic logic.. just simplify the given equation.

Just multiply, foil and simplify.

x+c=cx+x+c+1, cx+1=0, cx=-1, x=-1/c

x+c=cx+x+c+1, cx+1=0, cx=-1, x=-1/c