Skip to main content
Back

Rational Equations quiz

Control buttons has been changed to "navigation" mode.
1/15
  • What is a rational equation?
    A rational equation is an equation where a variable appears in the denominator of a fraction.
  • Why must we identify restrictions when solving rational equations?
    Restrictions are values that make the denominator zero, which are not allowed as solutions because division by zero is undefined.
  • What is the first step in solving a rational equation?
    The first step is to determine the restriction by setting the denominator equal to zero and solving for the variable.
  • How do you find the restriction for x in the equation x/(x-1) = 76?
    Set x-1 equal to zero, solve for x, and find that x cannot be 1.
  • What is the least common denominator (LCD) and why is it important?
    The LCD is the smallest expression that all denominators divide into, and it is used to eliminate fractions from the equation.
  • How do you eliminate fractions in a rational equation?
    Multiply every term in the equation by the LCD to clear the denominators.
  • After clearing denominators, what type of equation do you usually get?
    You usually get a linear equation, which can be solved using familiar algebraic methods.
  • What should you do after solving the linear equation for x?
    Check the solution against the restriction to ensure it does not make any denominator zero.
  • What happens if your solution equals the restriction?
    If your solution equals the restriction, there is no solution to the equation, and the solution set is the empty set.
  • How do you write the solution set when there is no solution?
    You write the solution set as the empty set, often denoted by ∅.
  • In the equation x-5/(x-2) = -3/(x-2) + 6, what is the restriction?
    The restriction is x cannot be 2, because x-2 in the denominator would be zero.
  • What is the LCD for the equation x-5/(x-2) = -3/(x-2) + 6?
    The LCD is x-2, since both denominators are x-2.
  • What is the result if you solve a rational equation and the solution is a restricted value?
    The equation has no solution, because the solution makes the denominator zero.
  • Why must you distribute the LCD to every term in the equation?
    You must distribute the LCD to every term to ensure all fractions are eliminated and the equation remains balanced.
  • What is the purpose of checking your solution against the restriction?
    Checking ensures your solution does not make any denominator zero, preventing undefined expressions.