after solving a rational equation, why is it important to check your answer? How is this done? What happens if you are checking a solution for the rational expression and find that it makes one of the denominators in the expression equal to zero?
It is important to check your answer after solving a rational equation in order to ensure that the obtained solution is valid and does not introduce any extraneous solutions. Checking is done to verify if the substituted value satisfies the original equation.
To check your answer after solving a rational equation, substitute the obtained solution back into the original equation and simplify both sides. If the simplified equation holds true, then the solution is valid. If the equation does not hold true, then the obtained solution is not valid and should be considered as an extraneous solution.
If, during the checking process, you find that the substituted value makes one of the denominators in the rational expression equal to zero, it means that the original equation is undefined at that point. This implies that the solution you obtained is not valid, as dividing by zero is undefined in mathematics. In such cases, you would need to exclude those values from the domain of the equation and consider them as extraneous solutions.
It is important to check your answer after solving a rational equation because sometimes the solutions may lead to extraneous solutions, which means they do not actually satisfy the original equation.
To check whether a solution is valid, you need to substitute the found value(s) back into the original rational equation and simplify both sides. If the resulting expressions are equal, then the solution is valid. If they are not equal, then the solution is not valid and should be discarded as an extraneous solution.
When checking a solution for a rational expression, if you find that it makes one of the denominators in the expression equal to zero, it implies that the original equation is undefined at that point. In such cases, the solution should be excluded or labeled as an excluded solution or a non-permissible value. This is because division by zero is undefined in mathematics. So if a solution makes any denominator equal to zero, it would lead to an undefined value in the rational expression.