Question

Which of the following values of x makes the rational expression below equal to zero? 2x+16/x+5

a. 5
b. -5
c. 8
d. -8

Answer 1

2x + 16 / x + 5
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 = -5 we have:
(2 (-5) +16) / ((- 5) +5)
(-10 + 16) / (- 5 + 5) = 6/0 (undefined)
Answer:
x = -5
b. -5

Answer 2

d. -8

Explanation:

Remember that you cannot possibly divide anything by 0, so if the denominator gives as a result 0, you are dealing with an impossibility, in order for a franction to give as a result 0, the numerator has to be 0, so we just need to equalize the numerator to 0 and solve for x to know how can we make the rational expression 0:

2x+16=0

2x=-16

x=-16/2

x=-8

So in order to make the expression equal to 0 x needs to be equal to -8,