Question

What values of the variable cannot possibly be solutions for the given​ equation, without actually solving the​ equation? StartFraction 6 Over 2 x plus 3 EndFraction minus StartFraction 1 Over x minus 7 EndFraction equals 0 6 2x+3− 1 x−7=0 Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A. The solutions cannot include nothing. ​(Simplify your answers. Type an integer or a fraction. Use a comma to separate answers as​ needed.)
B. There are no numbers that would have to be rejected as potential solutions.

Answer 1

Answer: Hello mate!

our equation in this problem is:

$\frac{6}{2x + 3} - \frac{1}{x - 7} = 0$

Now we have a rule in mathematics when the denominator is zero, the function is undefined (because you can not divide by zero). The two denominators that we have here are:

2x + 3 and x - 7, and now we can see for which values of x these denominators are zero in order to discard the values of x

1) 2x + 3 = 0

  x = -3/2 = -1.5

and

2) x - 7 = 0

   x= 7

(2x + 3); wich is equal to zero when x = -1.5 and x-7, wich is equal to zero when x = 7.

So just looking at these fractions you could assume that x = 7 and x= -1.5 are not possible solutions.