Question

I.

Encircle the number(s) that is (are) not in the domain of the given
rational algebraic expression.

-1/4x

-3
-1
0
4

Answer 1

see explanation

Explanation:

the denominator of a rational expression cannot be zero as this would make the expression undefined.

equating the denominator to zero and solving gives the value/s that x cannot be.

1

4x = 0 ⇒ x = 0

x = 0 ← is an excluded value in the domain

2

8x + 3 = 0

8x = - 3

x = -
`(3)/(8)`

x = -
`(3)/(8)` ← is an excluded value in the domain

3

2 - 10x = 0

- 10x = - 2

x =
`(-2)/(-10)` =
`(1)/(5)`

x =
`(1)/(5)` ← is an excluded value in the domain

4

x + 12 = 0

x = - 12

x = - 12 ← is an excluded value in the domain

5

(2x - 1)(x + 6) = 0

equate each factor to zero and solve for x

2x - 1 = 0

2x = 1

x =
`(1)/(2)`

x + 6 = 0

x = - 6

x = - 6 and x =
`(1)/(2)` ← are excluded values in the domain