The Composite in the Numerator

Two differentiable functions $g$ and $h$ are known only through this table of values:

$x$	$g(x)$	$g'(x)$	$h(x)$	$h'(x)$
$2$	$3$	$-4$	$7$	$6$
$3$	$1$	$5$	$5$	$2$

A third function is built out of them:

$F(x) = \frac{x\,h\!\left(g(x)\right)}{x^{2} + 1}$

Find $F'(2)$ .

Round your answer to two decimal places.