Suppose $a$ and $b$ from $\mathbb{R}$ as $a and $f$ and $g$ two continuous function on $[a;b]$ and derivable on $]a;b[$ as $\forall$ $x$ $\in$ $]a;b[$ $g{'}(x) \neq 0$.
How can I prove that $\exists$ $c$ $\in$ $]a;b[\;\;$ s.t. $\;\;\dfrac { f(b)-f(a) }{ g(b)-g(a) } =\dfrac { f^{ ' }\left( c \right) }{ g^{ ' }\left( c \right) } $ using Rolle's theorem.