Question

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

Answer 1

Answer: D.-6 and F.3

Step-by-step explanation:

The given rational number : $\dfrac{(x-3)(x+6)}{(x+7)}$

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

Let's check all the options :

A. 7

At x= 7  , $\dfrac{(7-3)(7+6)}{(7+7)}=\dfrac{26}{7}\neq0$

B. -7

At x= 7 ,  $\dfrac{(-7-3)(-7+6)}{(-7+7)}=\dfrac{10}{0}=\infty\neq0$

C. 6

At x= 6 ,  $\dfrac{(6-3)(6+6)}{(6+7)}=\dfrac{36}{13}\neq0$

D. -6

At x= -6 , $\dfrac{(-6-3)(-6+6)}{(-6+7)}=\dfrac{0}{1}=0$

E. -3

At x= -3 ,   $\dfrac{(-3-3)(-3+6)}{(-3+7)}=\dfrac{-9}{2}\neq0$

F. 3

At x= 3 , $\dfrac{(3-3)(3+6)}{(3+7)}=0$

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