Question

For which value(s) of x will the rational expression below equal zero? Check all that apply.

(x-3)(x+6)/x+7
A.7
B.-7
C.6
D.-6
E.-3
F.3

Answer 1

Answer: D.-6 and F.3

Explanation:

The given rational number :
`((x-3)(x+6))/((x+7))`

To find : The value of x , where the rational expression becomes equal zero.

Let's check all the options :

A. 7

At x= 7 ,
`((7-3)(7+6))/((7+7))=(26)/(7)\\eq0`

B. -7

At x= 7 ,
`((-7-3)(-7+6))/((-7+7))=(10)/(0)=\infty\\eq0`

C. 6

At x= 6 ,
`((6-3)(6+6))/((6+7))=(36)/(13)\\eq0`

D. -6

At x= -6 ,
`((-6-3)(-6+6))/((-6+7))=(0)/(1)=0`

E. -3

At x= -3 ,
`((-3-3)(-3+6))/((-3+7))=(-9)/(2)\\eq0`

F. 3

At x= 3 ,
`((3-3)(3+6))/((3+7))=0`

Thus, at x= -6 and 3 , the rational expression equals to zero .

So , the correct options are : D.-6 and F.3

Answer 2

If we assume you mean (x-3)(x+6)/(x+7), the expression is zero when the numerator factors are zero: at x=3 and x=-6.

Appropriate choices are ...

• D. -6
• F. 3