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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
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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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