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

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

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

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

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

Question

Emmanuel Obrien

Mathematics

16 March, 19:02

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

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

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

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

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

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Answers (1)

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Duarte · Answer 1

Answer: If a solution results in zero when subsitituted into the denominator of the equation, the solution is extraneous.

This is because you obtained the solution from a simplified version of the original equation, but you have to check if the solution obtained is a real solution of the original equation

In the case that when you substitute the solution in the original version the denominator becomes zero, this solution must be rejected, because the division by zero is not defined.