SOLUTION: What are extraneous solutions of an equation? Why do they sometimes occur in the process of solving rational or radical equations? can you provide examples?

Question 184295: What are extraneous solutions of an equation? Why do they sometimes occur in the process of solving rational or radical equations? can you provide examples?
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Extraneous solutions of an equation are EXTRA solutions that work in subsequent equations that are obtained in trying to solve an equation, but that do NOT work in the original equation!! These extraneous solutions are caused by squaring both sides of an equation or by multiplying both sides of an equation by an expression containing a variable.

For example, if you took the simple equation x=3, and square both sides, you would get x^2=9, which has two solutions, x=3 and x=-3. The second solution x=-3 is an extraeous solution in that it does NOT solve the original equation.

I have a TON of extraneous solutions on my website, which you can find by clicking on my tutor name "rapaljer" anywhere in algebra.com. Then look for my MATH IN LIVING COLOR pages, and choose Intermediate Algebra. Look for Section 2.07 on Fractional Equations, the last two problems that are posted there.

Also look for Section 3.07 Radical Equations! This one is LOADED with extraneous solutions!! I hope this helps!!

R^2
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