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