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Adding and Subtracting Rational Expressions
Slates!
Simplify .
Finding the Least Common Denominator
Observe:
Finding the LCD:
1) Factor the
denominators completely
2) Compute the LCD by
using every factor listed
as a factor of the LCD.
Use each factor the
greatest number of times
it is a factor in any of the
denominators.
Example 1: Find the least common denominator:
Example 2: Find the least common denominator:
Slates! Slates! Slates!
Find the Least Common Denominator :
Adding and Subtracting Rational Expressions
with Like Denominators
Rule for Adding / Subtracting Fractions
with Like Denominators
Fractions with like denominators are
added/subtracted by combining the
numerators algebraically and recording that
answer over a single denominator.
Example 1: Perform the indicated operation:
Example 2: Perform the indicated operation :
Practice: In your notes, work out the two
exercises. Then compare
your answers with the people sitting near you.
Some Rules of Algebra: Review
1. The same quantity can be added to both sides of
an equation without changing the equation.
2. Every term on both sides of an equation can be
multiplied ( or divided ) by the same quantity
without changing the equation.
3. The denominator and numerator of a fraction
can be multiplied by the same quantity without
changing the value of the fraction.
Fundamental Theorem of Fractions
Fundamental Theorem of Rational Expressions
The denominator and numerator of a fraction
can be multiplied by the same quantity
without changing the value of the fraction.
Steps:
1) Write fraction lines
2) Use LCD as new
denominator of each
term
3) Find new
numerators & combine
Adding and Subtracting Rational Expressions
with Unlike Denominators
Example 1: Perform the indicated operation:
Steps:
1) Write fraction lines
2) Use LCD as new
denominator of each term
3) Find new numerators & combine
Example 2: Perform the indicated operation:
Steps:
1) Write fraction lines
2) Use LCD as new
denominator of each term
3) Find new numerators & combine
Example 3: Perform the indicated operation:
Steps:
1) Write fraction lines
2) Use LCD as new
denominator of each term
3) Find new numerators & combine
Example 4: Perform the indicated operation:
Steps:
1) Write fraction lines
2) Use LCD as new
denominator of each term
3) Find new numerators & combine
Example 5: Perform the indicated operation:
Steps:
1) Write fraction lines
2) Use LCD as new
denominator of each term
3) Find new numerators & combine
Example 6: Perform the indicated operation:
Steps:
1) Write fraction lines
2) Use LCD as new
denominator of each term
3) Find new numerators & combine
Dictator/Scribe
Have a great day!
Homework on MathXL
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