2
QuizMultiple Choice

Rational Equations — Quiz

Question 2 • Mathematics III

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

Answer
A
If a solution results in zero when substituted into the denominator of the equation, the solution is extraneous.
B
If a solution results in a negative number when substituted into the denominator of the equation, the solution is extraneous.
C
When there is more than one solution, one of the solutions is extraneous.
D
When a solution is a fraction, the solution is extraneous.

Explanation

A rational expression is undefined when its denominator equals zero. Therefore, if a candidate solution makes any denominator in the original equation zero, it cannot be a valid solution and is extraneous; a negative denominator or a fractional solution is not automatically extraneous.

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