P'4 Part 1 Rational Expressions

1
P.4 (Part 1)Rational Expressions

• Our goals are to learn
• How to find the domain of an algebraic expression
• Simplify rational expressions

2
Find the domain

• The domain of an algebraic expression is the set
  of all real numbers for which the expression
  results in a real number, when the expression is
  evaluated at one of these numbers. In algebra we
  need to consider three situations (for now).
• Ask yourself three questions
• Is it a fraction?
• Set the denominator equal to zero and solve
• Say x ____
• Is it a radical?
• Set the inside part gt 0
• Solve for x
• If you answered no to the 1st two questions, then
  the domain is all real numbers

3
Examples Find the domain

• .
• .
• .

4
Practice Time!

• Now try problems 55-57 on your handout.

5
SHOWDOWN!

• Write the answer on your white board.
• When the teacher yells, Showdown, hold up your
  white board.

6
Find the domain. Write the domain in interval
notation.

• 5x2 2x 1
• Interval notation
• 3x3 2
• Interval notation
• .
• Interval
• .
• Interval

• 6x2 2x, x gt 0
• Interval notation
• .
• Interval notation
• .
• Interval
• .
• Interval

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Simplify the Rational Expression

• Factor the numerator and denominator
• Remember to pull out the GCF first!!!
• Find the domain.
• Set the denominator equal to zero and solve.
• This means that none of your solutions can equal
  this number. If they do, youll say NO
  SOLUTION
• Cancel out any common factors or common groups
• Watch out for NO SOLUTION answers
• Watch out for when you can use this trick
• 5 x -(x 5)

Factor out a negative
8
ExamplesSimplify the rational expression
9
Practice Time!

• Now try problems 58-60 on your handout.

10
Simplify the Rational ExpressionMultiply or
Divide

• Factor the numerator and denominator of all
  fractions
• Remember to pull out the GCF first!!!
• If it is a division problem Multiply by the
  Reciprocal
• Keep, Change, Flip
• Find the domain.
• Set the denominator equal to zero and solve.
• This means that none of your solutions can equal
  this number. If they do, youll say NO
  SOLUTION
• Cancel out any common factors or common groups
• Watch out for NO SOLUTION answers
• Write your answer as a single fraction.

11
ExamplesMultiply or Divide
12
Practice Time!

• Now try problem 63 on your handout.