Answer:
A:x=3
B:x=-4
Step-by-step explanation:
The domain is set of all values of x for which the given rational function is defined.
The rational equation is
[tex] \frac{50}{4x - 12} + \frac{x - 4}{ {x}^{2} + x - 12 } = \frac{x}{2} [/tex]
The rational function will not be defined if the denominator is zero.
That is if:
1.
[tex]4x - 12 = 0 \implies 4x = 12\implies \: x = 3[/tex]
2.
[tex] {x}^{2} + x - 12 = 0\implies (x - 3)(x + 4) [/tex]
This implies that x=3 or x =-4
Therefore the equation is defined on all real values of x, except x=3 or-4
