Question

For what value of x is the rational expression below equal to zero?

12-x/x-6

a. 9
b. 3
c. -9
d. -3

Answer 1

(12 - x)/(x - 6) = 0

(x - 6)[(12 - x)/(x - 6)] = 0(x - 6)

12 - x = 0

-x = -12

x = -12/-1

x = 12/1

x = 12

The correct answer is 12. When x = 12, the rational expression is 0.

If you are looking for the value of x that makes the rational expression undefined, then we set the denominator to 0 and solve for x.

The answer choices listed do not make the rational expression 0.

Don't believe me? Try it. Let x be the given choices and simplify. You will see that 9, 3, -9, and -3 do not make the rational expression 0.

Answer 2

-12

Explanation:

When you are looking for the value of a rational expression that is inside a fraction, you just have to take the numerator and make it equal to zero, since every time you divide zero by any number the resultant will be zero.

In the fraction
`(12-x)/(x-6)` the numerator is :(12-x)

So you equalize it to zero:

12-x=0

The next step you clear "x"

x=
`(-12)/(-1)`

x=12

So your answer is when X´s value is 12, your rational expression will be zero.