Final answer:
The restricted values of the rational expression x/(7x^2+6x) are x = 0 and x = -6/7.
Step-by-step explanation:
The restricted values of x for the rational expression x/(7x^2+6x) are the values of x that would make the denominator equal to zero since division by zero is undefined.
To find the restricted values, we set the denominator equal to zero and solve for x:
7x^2 + 6x = 0
Factoring out x from both terms:
x(7x + 6) = 0
Setting each factor equal to zero:
x = 0 or 7x + 6 = 0
The first solution is x = 0. To find the second solution, we solve the equation 7x + 6 = 0:
7x = -6
x = -6/7
Therefore, the restricted values of x for the rational expression are x = 0 and x = -6/7.