Why can x = 6 when all the other numbers would not allow this equation to work?

Question

x-6/x+4 divided by x+7/x+5. I know when -4, -5, and -7 are used as x will make the equation 0, but why can 6 be used as x?

Answer 1

If you get a zero for the numerator, you will always get zero for an answer. If you use a zero in the denominator, it is considered as undefined.

Answer 2

6 is the only valid answer because any other answer gives you a zero in the denominator.

((x-6)/(x+4))/((x+7)/(x+5))

If x = -4

(-10/0)/(1/-1) = undefined/-1 = undefined

If x = -5

(-11/-1)/(2/0) = 11/undefined = undefined

If x = -7

(-13/-3)/(0/-2) = (13/3)/0 = undefined

So x = 6 is the only possible solution.

Answer 3

actually your equation is equal to
(x-6)(x-5)/(x+4)(x+7) this means that 6 is a valid solution because 0*(x-5)=0 but -7 is not because that will cause a zero denominator.