Rational Equations Unit - Notes
Add & Subtract
Graphing
Solve
Must have common denominators
Rational
Equations
Multiply every term by the LCD
to get rid of denominator
Algebra 3-4 PLC © 2015 Fairfax Math Department
Multiply & Divide
Factor and Reduce
Rational Equations Unit - Notes
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Multiplying and Dividing Rational Expressions
A rational expression is in simplified form provided its numerator and denominator have
no common factors. To simplify a rational expression, apply the following property.
Let a, b, and c be nonzero real numbers or variable expression.
Then the following property applies:
MULTIPLICATION ALGORITHM:
1) Factor everything to simplest terms
2) Cross cancel any common factors
3) Simplify your answer
DIVISION ALGORITHM:
1) Take the reciprocal of the divisor, then multiply
2) Factor everything to simplest terms
3) Cross cancel any common factors
4) Simplify your answer
Algebra 3-4 PLC © 2015 Fairfax Math Department
Rational Equations Unit - Notes
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Adding and Subtracting Rational Expressions
Algorithm:
1) Factor all denominators to lowest terms
2) Identify the Least Common Denominator (LCD)
3) Adjust denominators and numerators
4) Add or Subtract Numerators
5) Simplify (reduce) if possible
Examples:
Algebra 3-4 PLC © 2015 Fairfax Math Department
Rational Equations Unit - Notes
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Complex Fractions
A complex fraction is a fraction that contains a fraction in its numerator or denominator.
Algorithm:
A complex fraction consists of three separate problems, the numerator, the dominator and the division problem.
Numerator
1. Identify the common denominator for the fractions in the numerator.
2. Adjust the numerators and denominators
3. Add or subtract the numerators
4. Reduce if possible
Denominator
1. Identify the common denominator for the fractions in the denominator.
2. Adjust the numerators and denominators
3. Add or subtract the numerators
4. Reduce if possible
Division
1. Take the reciprocal of the denominator and multiply
2. Cross-cancel if possible
3. Write your answer in simplified form
Algebra 3-4 PLC © 2015 Fairfax Math Department
Rational Equations Unit - Notes
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Solve Rational Equations
Algorithm:
1. Identify the Least Common Denominator (LCD)
2. Multiply every term by the LCD
3. Simplify
4. Solve
Examples:
Factor the denominators
Multiple each term by the common denominator
Cancel and simplify
Algebra 3-4 PLC © 2015 Fairfax Math Department
Rational Equations Unit - Notes
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Graphing Simple Rational Functions
All rational functions in the form
have graphs that are hyperbolas with asymptotes at (vertical) and (horizontal).
Algorithm:
1. If the rational function is written in ‘simple’ form, then proceed to step 2.
2. Identify the vertical and horizontal asymptotes.
3. Draw and label the asymptotes.
4. Make a t-chart, using two points from each side of the vertical asymptote.
5. Plot the points and draw the hyperbola.
Algebra 3-4 PLC © 2015 Fairfax Math Department
Rational Equations Unit - Notes
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Graphing Rational Equations
Algebra 3-4 PLC © 2015 Fairfax Math Department