True they are exactly the same thing.

False, they are completely different because the second expression did not state the restrictions.

Ex 3: $$-\frac{\left(x-4\right)}{\left(x+3\right)};\ x\ne-2$$

Ex 4: $$5\left(x+1\right);\ x\ne1$$

Ex 3: $$-\frac{\left(x+4\right)}{\left(x-3\right)};\ x\ne2,\ 3$$

Ex 4: $$5\left(x+1\right);\ x\ne1$$

Ex 3: $$\frac{\left(x+4\right)}{\left(x+3\right)};\ x\ne-2$$

Ex 4: $$5\left(x+1\right);\ x\ne-1$$

Ex 3: $$\frac{\left(x-4\right)}{\left(x+3\right)};\ x\ne-2$$

Ex 4: $$5\left(x+1\right);\ x\ne1$$