- What is a Complex Fraction?
- A complex fraction is a rational expression whose numerator and denominator are themselves rational expressions.
- Since the numerator and denominator of the complex fraction are fractions themselves, the numerator and denominator are each called secondary fractions.
- Simplifying Complex Fractions
- The steps for 2 methods of simplifying complex fractions are given here.
- Method 1: Multiplying by a Common Denominator
- Find the lowest common denominator of the two secondary fractions.
- Multiply both the numerator and denominator of the complex fraction by this lowest common denominator.
- Simplify (reduce to lowest terms) the resulting rational expression.
- Method 2: Simplifying Numerator and Denominator
- Simplify (reduce to lowest terms) each secondary fraction.
Solving Rational Equations
- What is a Rational Equation?
- A rational equation is an equation that contains at least one rational expression.
- To Solve a Rational Equation......
- Determine the lowest common denominator of all rational expressions in the equation.
- Multiply both sides of the equation by the lowest common denominator.
- Simplify by removing parentheses and combining like terms.
- Solve the equation resulting from step 4.
- Check the solution in the original equation. This step is essential since it is here that you will eliminate extraneous solutions (see below).
- What are Extraneous Solutions?
- An extraneous solution is a value that you think is a solution because it was found by the solving process but, this value does not solve the original equation.
- The way that you determine that a value is an extraneous solution is by checking that value in the original equation:
- If a value that you think is a solution does not solve the original equation, then that value is an extraneous solution.
- The check step is where extraneous solutions are found.
- Always check all solutions in the original equation to make sure they solve the originalequation.