Algebra II Recipe: Solving Rational Equations
A. An Equation with One Solution, an Extraneous Solution, or Two solutions.
1. Determine the LCD.
2. Multiply each term in the equation by the LCD.
3. Solve the equation for the variable.
• If the equation becomes quadratic, solve it by factoring or by using the quadratic formula.
• If the original equation is a simple rational equation or two rational expressions set equal to each other, cross-multiply to solve.
4. Check the solution(s) into the original equation.
• If a single solution does not check into the original equation, the solution is considered an extraneous solution and the original equation has no solution.
• If two solutions are being checked, both solutions may check, only one of the solutions may check, or neither solution may check. If neither solution checks, both are considered extraneous solutions and the original equation has no solution.
Examples:
B. Adding and Subtracting with Unlike Denominators
1. Factor each denominator.
2. Multiply the numerator and denominator of each fraction by the factor or factors that its denominator is missing.
3. Write the result of all the multiplying. (Leave the denominator in factored form.)
4. Add or subtract the numerators.
5. Put the result over the common denominator.
6. Simplify the fraction if possible.
Examples:
C. Simplifying a Complex Fraction
1. Write the numerator and denominator as single fractions by adding or subtracting.
2. Rewrite the problem changing the main fraction bar to a division symbol.
3. Change the division problem to multiplying by the reciprocal.
4. Simplify completely.
Examples:

G Redden

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