how do you solve if x(5+root7) is a rational number then x must be equal to?

Let x = a + b√7, where a and b are real numbers.

(a + b√7)(5 + √7)
= 5a + a√7 + 5b√7 + 7b
= (5a + 7b) + (a + 5b)√7

When (a + b√7)(5 + √7) is real, a + 5b = 0
Then, a = -5b
When b = -n: a = 5n, where n is any real number

x = 5n - n√7
where n is any real number

x(5 + √7) = a/b . . . . . . where a and b are integers

x = a/b(5 + √7)

ie x is any rational number dived by (5 + √7)

the rational number divided with 5 + root7.
I don't get the purpose of the question.