Question

Heather wrote this solution to solve for x.

Which statement is true?
O
-1 is an extraneous solution because it creates a 0
in the denominator.
5 is an extraneous solution because it creates a 0 in
the denominator.
There are no extraneous solutions.
Both 1 and 5 are extraneous solutions because
they create a 0 in the denominator.

Answer 1

The correct statement is there are no extraneous solutions.

The correct statement is there are no extraneous solutions.

This is because both 3 and -4 satisfy the original equation (
`x^2` + x - 12 = 0) without creating any 0 in the denominator. Neither value makes any term in the equation undefined.

Therefore, both solutions are genuine and there are no extraneous solutions.