Precalculus A Fuctional Approach to Graphing and Problem Solving

Section 4.3: Real Roots of Rational and Radical Equations
Essential Ideas
  • To solve a rational equation:
    Step 1 Exclude values that cause division by zero.
    Step 2 Multiply both sides by the least common dominator and simplify
    Step 3 Solve the resulting equation
    Step 4 Check each solution to make sure it is not one of the excluded
               values; that is, division by zero is not permitted. Any value that is
               excluded in this manner is called an extraneous root.

  • Property of Powers
    If P and Q are algebraic expressions in a variable x, and n is any positive integer, then the solution set of P = Q is a subset of the solution set of
    P n = Q n. The equation P n = Q nis called a derived equation of P = Q.

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© 2011 Karl J. Smith. All rights reserved.