# 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:

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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