Why is it necessary to perform a check when solving rational equations?

Jayde I already told you that you must perform a check because you may get answers that do not check out in the original equation.

Apparently you do not believe me so if anyone else would explain to her!

But Mom I want to make sure!

Mom is right. This happens often when during the operation you square something, or take the square root of something.

Thank you Mr. Bob (& Mom) but I had to check! :)

double checking your work is a good idea because if you made an error, say that you meant to write one number and accidently wrote another number, that would throw the whole equation off. If you check your answer, you will catch the error.

Performing a check when solving rational equations is necessary to ensure the validity and correctness of your solution. Rational equations involve fractions, and there are a few reasons why performing a check is essential:

1. Avoiding Extraneous Solutions: Sometimes, when solving rational equations, you may end up with extraneous solutions. These are values that satisfy the equation after simplification but are not valid solutions to the original equation. A check helps to eliminate such extraneous solutions.

2. Verifying the Solution: By performing a check, you ensure that the solution you obtained is correct. It helps to validate that the values you found satisfy the equation and make both sides of the equation equal.

3. Identifying Domain Restrictions: Rational equations often have restrictions on the domain, where certain values of the variable may cause division by zero. By performing a check, you can identify any potential restrictions and ensure that the solution you obtained falls within the allowed domain.

To perform a check:

1. Substitute the values you obtained for the variables back into the original equation.

2. Simplify both sides of the equation using the given values.

3. If the simplified expressions on both sides of the equation are equal, then the solution is valid. However, if they are not equal, then you have made an error or obtained an extraneous solution.

Performing this check will give you confidence in the correctness of your solution and help you avoid common mistakes when solving rational equations.