When solving a rational equation, why is it necessary to perform a check?
If you mean something like
x^2 = 25
then x = +5 or x = -5
only one of the two solutions may solve your original problem. Therefore you try them both in the original problem that led to x^2 = 25 to see if one or the other or both works.
Basically to see if the value found for x will yield the same answer on both sides of the equation.
When solving a rational equation, it is necessary to perform a check to ensure that the obtained solution is valid. This is because rational equations involve fractions, and sometimes the process of solving the equation can lead to extraneous solutions, which are solutions that do not satisfy the original equation.
To perform a check, you need to substitute the obtained solution back into the original equation and simplify both sides of the equation to see if they are equal. If they are equal, then the solution is valid. If they are not equal, then the solution is not valid and is considered an extraneous solution.
Performing a check is important for the following reasons:
1. Avoiding mistakes: Mistakes can happen during the process of solving an equation, such as making a calculation error or forgetting to consider certain restrictions. Performing a check helps to catch any mistakes made during the solving process.
2. Confirming the validity: Rational equations may have restrictions on the domain, such as denominators that can't be zero. Performing a check ensures that the obtained solution satisfies these restrictions and is a valid solution.
3. Identifying extraneous solutions: In some cases, solving a rational equation can lead to solutions that do not actually satisfy the original equation. These are called extraneous solutions. By performing a check, you can identify whether the obtained solution is valid or extraneous.