Answer
The value of given expression is $6x+3h-1$.
Work Step by Step
Substitute the value of $f\left( x \right)=3{{x}^{2}}-x+5$ in the main expression:
$\begin{align}
& \frac{f\left( x+h \right)-f\left( x \right)}{h}=\frac{3{{\left( x+h \right)}^{2}}-\left( x+h \right)+5-\left( 3{{x}^{2}}-x+5 \right)}{h} \\
& =\frac{3\left( {{x}^{2}}+2xh+{{h}^{2}} \right)-x-h+5-3{{x}^{2}}+x-5}{h} \\
& =\frac{3{{x}^{2}}+6xh+3{{h}^{2}}-x-h+5-3{{x}^{2}}+x-5}{h} \\
& =6x+3h-1
\end{align}$
Thus, the value of given expression is $6x+3h-1$.
