To solve a rational equation, follow these steps:
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Identify any restrictions on the variable. Look for values of the variable that would make the denominator equal to zero. These values are not allowed in the solution.
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Multiply both sides of the equation by the common denominator of all the fractions in the equation. This will eliminate the fractions and leave you with a polynomial equation.
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Simplify the resulting equation by combining like terms and moving all terms to one side of the equation.
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Solve the simplified equation by factoring, using the quadratic formula, or any other appropriate method.
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Check your solution(s) by substituting them back into the original equation and ensuring that both sides of the equation are equal.
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If any of the solutions violate the restrictions identified in step 1, they are not valid solutions.
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Write the final solution(s) in the form of a set of numbers or an interval, depending on the context of the problem.
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