Alg2 with Trig CC Unit 3
Unit 3: Rational Functions
Lesson #3:
Complex
Fractions
Lesson 3: Complex Fractions
A complex fraction is a fraction in
which the numerator, denominator, or
both, also contain fractions.
If the expression contains a variable, it is
called a complex rational expression.
Examples:
Lesson #3: Complex Fractions
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Alg2 with Trig CC Unit 3
Complex Fractions
Complex fractions always
need to be simplified.
How are complex fractions simplified?
A complex fraction is
simplified when the
expression no longer has
a fraction in its numerator
and/or denominator.
A complex fraction is
simplified by multiplying
the fraction by the least
common denominator of
the fraction.
Complex Fractions
To Simplify a Common Fraction by
Multiplying by a Common Denominator:
LCD:
Lesson #3: Complex Fractions
Steps:
1. Find the least common
denominator (LCD) of all fractions
appearing within the complex
fraction.
2. Multiply both the numerator and
the denominator of the complex
fraction by the LCD from step 1.
3. Simplify whenever possible.
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Alg2 with Trig CC Unit 3
Complex Fractions
To Simplify a Common Fraction by
Multiplying by a Common Denominator:
· Zoom In:
Numerator
Continued:
2. Multiply both the numerator and
the denominator of the complex
fraction by the LCD from step.
3. Simplify whenever possible.
·
Distribute!
Denominator
Eliminated
Complex
Fraction!
· What ⇒
happened?
Complex Fractions
To Simplify a Common Fraction by
Multiplying by a Common Denominator:
Continued:
Fraction needs
to be further
simplified!
3. Simplify whenever possible.
How?
⟹ Factor!
Lesson #3: Complex Fractions
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Alg2 with Trig CC Unit 3
Examples: Simplify each
complex rational expression.
Ex 1) ·
Need the LCD for the entire expression!
LCD: Eliminated
Complex
Fraction!
⟹ Factor!
⟹ Simplify!
Distribute!
Examples: Simplify each
complex rational expression.
Ex 2) ·
LCD: Recall:
Recall: “cousins”
Lesson #3: Complex Fractions
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Alg2 with Trig CC Unit 3
Examples: Simplify each
complex rational expression.
Ex 3) LCD: ·
Examples: Simplify each
complex rational expression.
Ex 4) ·
LCD: Lesson #3: Complex Fractions
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Alg2 with Trig CC Unit 3
Examples: Simplify each
complex rational expression.
Ex 5) LCD: Are we finished??
⟹ NO!
Can you divide here?⟹
· ⟹ Simplify numerator &
NO!
denominator individually!
Examples: Simplify each
complex rational expression.
Ex 5) Lesson #3: Complex Fractions
Are we finished??
⟹ NO!
Fraction needs to be
further simplified!
How?
⟹ Factor!
Question: What is a
step that we did not
necessarily have to
do?
⟹ Multiply denominator
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Alg2 with Trig CC Unit 3
Examples: Simplify each
complex rational expression.
Ex 6)
LCD: · Examples: Simplify each
complex rational expression.
Ex 6)
Can you divide here?
⟹ NO!
⟹ GCF!
⟹ Simplify numerator &
denominator individually!
How?
⟹ Factor!
⟹Simplify numerator & denominator!
Lesson #3: Complex Fractions
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Alg2 with Trig CC Unit 3
Examples: Simplify each
complex rational expression.
Ex 6)
⟹ Factor!
⟹ Can we divide here?
NO!
Examples: Simplify each
complex rational expression.
Ex 7) Lesson #3: Complex Fractions
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