Question

Find the restricted values of x for the following rational expression, If there are no restricted values of x, indicate "No Restrictions" Separate multiple answers with commas.

Answer 1

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:

`(6x)/(2x^2-5x)`

we need to find when:

`2x^2-5x=0`

Solving this equation we have that:

`\begin{gathered} 2x^2-5x=0 \\ x(2x-5)=0 \end{gathered}`

the last equivalent expression implies that:

`\begin{gathered} x=0 \\ or \\ 2x-5=0 \\ 2x=5 \\ x=(5)/(2) \end{gathered}`

Therefore the restricted values of x are 0 and 5/2