Question

Which of the following values of x makes the rational expression below undefined? x-25/x+13

a. 13
b. 0
c. 25
d. -13

Answer 1

Option D

Explanation:

We will check each option for the given expression (x-25)/(x+13)

(A). for x = 13

`((x-25)/(x+13))=(13-25)/(13+13) =(-12)/(26)`

So expression is defined.

(B). for x = 0

`(x-25)/(x+13)=(0-25)/(0+13) =((-25)/(13))`

So expression is defined.

(C). For x = 25

`((x-25)/(x+13))=(25-25)/(25+13) =0`

So expression is defined

(D). For x = -13

`(x-25)/(x+13)=(-13-25)/(-13+13)=( (-38)/(0))`

Function is not defined.

Option D is the answer.

Answer 2

x-25 / x + 13
For this case what you should know is that an indefinite expression are those in which mathematically no numerical value can be obtained.
We have then that a division between zero causes an expression to be undefined.
For x = -13 we have:
(-13-25) / (- 13 + 13) = - 38/0 (undefined)
Answer:
x = -13
d. -13