Question

What causes a solution to a rational equation to be an extraneous solution?

A) When there is more than one solution, one of the solutions is extraneous.

B) If a solution results in zero when substituted into the denominator of the equation, the solution is extraneous.

C) If a solution results in a negative number when substituted into the denominator of the equation, the solution is extraneous.

D) When a solution is a fraction, the solution is extraneous.

Answer 1

B) If a solution results in zero when substituted into the denominator of the equation, the solution is extraneous.

Explanation:

An extraneous solution is a solution that emerges from the problem, but it's not actually a solution because it doesn't make sense to the problem.

The best example of this is when we get a solution in a rational expression which becomes the denominator zero. That's an extraneous solution because it doesn't make sense, since the number zero can't divide a number.

Therefore, the right answer is B.

Answer 2

When there is more than one solution, one of the solutions is extraneous.