Question

Find any domain restrictions on the given rational equation:

Answer 1

Answer:

$\dfrac{x}{2 \cdot x + 14} + \dfrac{x - 4}{6} = \dfrac{3}{x^2} + 2\cdot x - 35; Domain \ restriction \ x \neq 0 \ or \ -7$

Step-by-step explanation:

The given rational equation is presented here as follows;

$\dfrac{x}{2 \cdot x + 14} + \dfrac{x - 4}{6} = \dfrac{3}{x^2} + 2\cdot x - 35$

A domain restriction are the limits to the ranges of input values (x-values) of a function

The three main types of domain restrictions are the reciprocal function, the log function, and the root function

The form of restriction in the given rational are reciprocal form, which are;

$\dfrac{x}{2 \cdot x + 14}$, and $\dfrac{3}{x^2}$, from which the function is undefined when;

2·x + 14 = 0, therefore when x = -7, or x² = 0, when x = 0

Therefore, the domain restrictions are that the function is defines for all x, except x = -7 and x = 0

The domain restrictions are x ≠ -7 and x ≠ 0.