Question

Question 7 of 10
Find any domain restrictions on the given rational equation:
X-4+50
4x-12x²+x-12 2
Select all that apply.
A. x = 0
B. x = 3
C. x = 4
D. x = -4

Answer 1

The domain restrictions on the rational function $\frac{50}{4x - 12} + \frac{x- 4}{x^2 + x - 12} = \frac{x}{2}$ are (b) x = 3 or and (d) x = -4

How to determine the domain restrictions?

The function as expressed in the correct format is:

$\frac{50}{4x - 12} + \frac{x- 4}{x^2 + x - 12} = \frac{x}{2}$

Factorize the denominators of the fractions

$\frac{50}{4(x - 3)} + \frac{x- 4}{x^2 + 4x- 3x - 12} = \frac{x}{2}$

Factor out x and -3

$\frac{50}{4(x - 3)} + \frac{x- 4}{x(x + 4)- 3(x + 4)} = \frac{x}{2}$

Factor out x + 4

$\frac{50}{4(x - 3)} + \frac{x- 4}{(x- 3)(x + 4)} = \frac{x}{2}$

Set the denominators to 0

4(x - 3) = 0

(x - 3)(x + 4) = 0

Solve for x:

4(x - 3) = 0 ⇒ x = 3

(x - 3)(x + 4) = 0 ⇒ x = 3 or x = -4

This means that the domain restrictions on the rational function are (b) x = 3 or and (d) x = -4

Read more about domain restrictions at:

https://brainly.com/question/14883326

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