5.2  Radical and Rational Functions

Radical and Rational Functions

Rational Expressions Vs Rational Equations

    Rational expressions are different from rational equations.

Rational Expressions

    Rational Expression solutions will always have a denominator.
    You are not solving for x.
    You are adding or subtracting the rationals, so keep the denominator in the answer.

Rational Equations

   Rational Equation solutions will NOT have a denominator in the answer.
      You ARE solving for x, so we must look for a common denominator to eliminate the denominator.
      Multiply both sides by the common denominator and work with the remaining numerator solving for x.

Add/Subtract Rationals

      ~ To add the two fractions, you need to determine the common denominator.

     ~  In the problem below, the common denominator is  (x - 2) (x + 2).

     ~  The second fraction is missing one of the factors (x - 2).  You need to multiply the second fraction by (x - 2).

     ~  Using the above information, look over the problem below to recall how to add two rationals.

Solving Rational Equations

   ~  The problem below is an equation.

   ~  Eliminate the denominator by multiplying both sides of the equation by the least common denominator.

   ~  This will eliminate the denominator and leave us working with a numerator. 

   ~  We will be multiplying the numerators by the missing factors.

    ~  Combine similar terms and solve for x.

Important: Check to make sure the values of x are solutions for the equation.

    ~  Using the above information, look over the problem below to recall how to solve rational equations.