2. Add:
Simplify and state the domain.

see explanation

Step-by-step explanation:

+ ← factor the denominators

= +

= + ← simplify numerator

=

=

The denominator cannot be zero as this would make the rational function undefined

Equating the denominator to zero and solving gives the values of x that cannot be in the domain

5(x + 2)(x - 4) = 0

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 4 = 0 ⇒ x = 4

x = - 2, x = 4 ← excluded values

domain : x ∈ R ( x ≠ - 2, x ≠ 4 )

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step-by-step explanation:

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