To find the restricted values for a rational function we need to determine for which values of x the denominator is zero, this values are the restricted values. This comes from the fact that we can't divide by zero.
With this in mind, for the expression:
[tex]\frac{6x}{2x^2-5x}[/tex]
we need to find when:
[tex]2x^2-5x=0[/tex]
Solving this equation we have that:
[tex]\begin{gathered} 2x^2-5x=0 \\ x(2x-5)=0 \end{gathered}[/tex]
the last equivalent expression implies that:
[tex]\begin{gathered} x=0 \\ or \\ 2x-5=0 \\ 2x=5 \\ x=\frac{5}{2} \end{gathered}[/tex]
Therefore the restricted values of x are 0 and 5/2
