W A T K I N S - J O H N S O N C O M P A N Y Semiconductor Equipment Group

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Chabot Mathematics
6.3 ComplexRational Fcns
Bruce Mayer, PE Licensed Electrical Mechanical
EngineerBMayer_at_ChabotCollege.edu
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Review

• Any QUESTIONS About
• 6.2 ? Add-n-Sub Rational Expressions
• Any QUESTIONS About HomeWork
• 6.2 ? HW-24

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Complex Rational Expression

• Complex Rational Expression is a rational
  expression that contains rational expressions
  within its numerator and/or its denominator.
• Some examples

The rational expressions within each complex
rational expression are red.
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Simplify Complex Rational Expressions by Dividing

1. Add or subtract, as needed, to get a single
   rational expression in the numerator.
2. Add or subtract, as needed, to get a single
   rational expression in the denominator.
3. Divide the numerator by the denominator (invert
   and multiply).
4. If possible, simplify by removing any factors
   equal to 1

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Example ? Simplify

• SOLUTION

Rewriting with a division symbol
Multiplying by the reciprocal of the divisor
(inverting and multiplying)
Factoring and removing a factor equal to 1.
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Example ? Simplify

• SOLUTION

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Solution cont.
Rewriting with a division symbol. This is often
done mentally.
Multiplying by the reciprocal of the divisor
(inverting and multiplying)
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Example ? Simplify

• SOLUTION Write the numerator and denominator as
  equivalent fractions.

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Simplify Complex Rational Expressions by LCD Mult.

1. Find the LCD of ALL rational expressions within
   the complex rational expression.
2. Multiply the complex rational expression by a
   factor equal to 1. Write 1 as the LCD over itself
   (LCD/LCD).
3. Simplify. No fractional expressions should
   remain within the complex rational expression.
4. Factor and, if possible, simplify.

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Example ? Simplify

• SOLUTION - In This Case look for the LCD of all
  four Terms.

Multiplying by a factor equal to 1, using the
LCD 12/121
Multiplying the numerator by 12 Dont forget the
parentheses! Multiplying the denominator by 12
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Solution cont.
Using the distributive law
Simplifying
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Example ? Simplify

• SOLUTION - The LCD for all is x

Using the distributive law

• When we multiply by x, all fractions in the
  numerator and denominator of the complex rational
  expression are cleared

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Example ? Simplify

• SOLUTION

The LCD for all is x3 so we multiply by 1 using
x3/x3.
Using the distributive law
All fractions have been cleared and simplified.
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Example ? Simplify

• SOLUTION Multiply the numerator and
  denominator by the LCD of all the rational
  expressions 2x here

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Example ? Simplify

• SOLUTION

Multiplying by 1, using the LCD.
Multiplying the numerator and the denominator.
Remember to use parentheses.
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Example ? Simplify
Using the distributive law to carry out the
multiplications

• SOLNcont.

Removing factors that equal 1. Study this
carefully. Take CARE with CANCELLING
Simplifying
Factoring. This does not simplify further
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Example ? Simplify

• SOLUTION Rewrite using only positive exponents

LCD of all individual Rational Expressions is x3y3
Simplified Version is still a bit Complex
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WhiteBoard Work

• Problems From 6.3 Exercise Set
• 38, 42, 48, 53

• Three Resistorsin Parallel

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All Done for Today

• Liquid Crystal Display

More Infoon LCDs
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Chabot Mathematics
Appendix
Bruce Mayer, PE Licensed Electrical Mechanical
EngineerBMayer_at_ChabotCollege.edu

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Graph y x

• Make T-table

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