Checking your solutions after solving a rational expression is crucial to ensure accuracy and identify any extraneous solutions that may arise, particularly when dealing with variables in the denominator. This step helps confirm that the solutions do not make the denominator zero, which would render the expression undefined. Additionally, verifying your solutions can help catch algebraic errors made during the solving process. Ultimately, it reinforces the correctness and reliability of your final answer.
To solve problems involving rational algebraic expressions, first, identify any restrictions by determining values that make the denominator zero. Next, simplify the expression by factoring and reducing common factors. If the problem involves equations, cross-multiply to eliminate the fractions, then solve for the variable. Finally, check your solutions against the restrictions to ensure they are valid.
When factoring, we can check our work by expanding the factored expression to see if it simplifies back to the original polynomial. Additionally, we can substitute specific values for the variable to ensure that both the original and factored forms yield the same results. Finally, using the Rational Root Theorem can help verify that any rational roots of the polynomial match those derived from the factored expression.
You should check whether you can simplify the answer.
To solve rational expressions, first, factor both the numerator and the denominator whenever possible. Next, identify any common factors that can be canceled out to simplify the expression. If the expression includes an equation, set the simplified form equal to zero to find the variable's value, and ensure to check for any excluded values that make the denominator zero. Finally, express the solution in its simplest form.
If the solution, makes the denominator equal to zero, makes the expression of a logarithm or under a square root, a negative one. If there are more than one denominator, check all the solutions. Usually, we determine the extraneous solutions before we solve the equation.
To solve problems involving rational algebraic expressions, first, identify any restrictions by determining values that make the denominator zero. Next, simplify the expression by factoring and reducing common factors. If the problem involves equations, cross-multiply to eliminate the fractions, then solve for the variable. Finally, check your solutions against the restrictions to ensure they are valid.
It is important to check your answers to make sure that it doesn't give a zero denominator in the original equation. When we multiply both sides of an equation by the LCM the result might have solutions that are not solutions of the original equation. We have to check possible solutions in the original equation to make sure that the denominator does not equal zero. There is also the possibility that calculation errors were made in solving.
You should check whether you can simplify the answer.
To solve rational expressions, first, factor both the numerator and the denominator whenever possible. Next, identify any common factors that can be canceled out to simplify the expression. If the expression includes an equation, set the simplified form equal to zero to find the variable's value, and ensure to check for any excluded values that make the denominator zero. Finally, express the solution in its simplest form.
If the solution, makes the denominator equal to zero, makes the expression of a logarithm or under a square root, a negative one. If there are more than one denominator, check all the solutions. Usually, we determine the extraneous solutions before we solve the equation.
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The rational numbers form a field. In particular, the sum or difference of two rational numbers is rational. (This is easy to check directly). Suppose now that a + b = c, with a rational and c rational. Since b = c - a, it would have to be rational too. Thus you can't ever have a rational plus an irrational equalling a rational.
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If its decimal representation is either terminating or a repeating number then it is rational. Otherwise it is irrational.
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It doesn't have a square root, or check mark symbol
It often helps to isolate the radical, and then square both sides. Beware of extraneous solutions - the new equation may have solutions that are not part of the solutions of the original equation, so you definitely need to check any purported solutions with the original equation.