Let $f(x)=\frac{5}{x- 3}$. Then according to the definition of derivative
$\displaystyle f'(x) = \lim_{t\to x}$
(Your answer above and the next few answers below will involve the variables $t$ and $x$.)
The expression inside the limit simplifies to a simple fraction with
numerator $=$
and denominator $=$
We can cancel the factor appearing in the denominator against a similar factor appearing in the numerator leaving a simpler fraction with
numerator $=$
and denominator $=$
Taking the limit of this fractional expression gives us
$f'(x) =$

You can earn partial credit on this problem.