Question

When solving a rational equation, why is it necessary to perform a check? Answer in 50 words or more please. Thanks :)

Answer 1

Because an invalid operation has been performed. Two of the most common examples are multiplication by zero (to remove fractions) and squaring both sides of an equation (to remove radicals). These procedures result in extraneous solutions.

Extraneous solutions could be avoided by the use of correct procedures, but they are not taught, as it is thought to be easier to check the answers at the end.

Examples:

Incorrect: (P/Q = 0) ≡ (P = 0)
Correct: (P/Q = 0) ≡ (P = 0 and Q ≠ 0)

Incorrect: (√P = Q) ≡ (P = Q^2)
Correct: (√P= Q) ≡ (P = Q^2 and Q ≥ 0)

Answer 2

does that help?

Answer 3

Thank you.