math test 2

Rational Expressions

• A rational expression is a fraction in which the numerator and the denominator are both polynomials.
• To work with rational expressions, the following operations can be performed:
  1. Addition: To add two rational expressions, find a common denominator.
  2. Subtraction: Similar to addition, use a common denominator.
  3. Multiplication: Multiply numerators and denominators.
  4. Division: Multiply by the reciprocal of the divisor.

Simplifying Rational Expressions

• Factor both the numerator and denominator and then cancel common factors.
• Be cautious of restrictions where the denominator cannot equal zero.

Radical Expressions

• A radical expression involves roots, such as square roots, cube roots, etc.
• Simplifying Radical Expressions: To simplify
  • Factor out the largest square (or cube, etc.) possible.
  • Use rules of radicals to combine or simplify terms.

Radical Equations

• An equation that includes a variable within a radical.
• Solve by first isolating the radical and then squaring both sides.
• Check for extraneous solutions, as squaring can introduce solutions not valid in the original equation.