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Review of Addition and Subtraction of fractions

and Introduction to Simplifying Complex

Fractions

Review of Addition, Subtraction of Fractions

- To add or subtract rational expressions, a common

denominator is necessary... - Example Simplify

Find the LCD 6x

Now, rewrite the expression using the LCD of 6x

Simplify...

Add the fractions...

19 6x

Lets try one with polynomials as denominators...

- Example Simplify

Find the LCD

(x 2)(x 2)

Rewrite the expression by multiplying the top and

bottom of each fraction by whatever is required

to get the LCD of (x 2)(x 2)

Simplify... (watch out for the negative!)

5x 22 (x 2)(x 2)

Complex Fraction a fraction with a fraction in

the numerator and/or denominator.

- Such as
- How would you simplify this complex fraction?
- Multiply the top by the reciprocal of the bottom!

Method 1For simplifying Complex Fractions

- Work on the numerator and denominator separately.
- Find the common denominator of the fractions on

the top and combine them. - Find the common denominator of the fractions on

the bottom and combine them. - Invert the bottom and multiply by the top.
- Simplify where possible.

Example

Invert the bottom and multiply

Another Example

Yet another example

Method 2 For simplifying Complex Fractions

- To simplify complex fractions, find the LCD of

all the little fractions - Multiply every term by the LCD of all the little

fractions ... - Simplify
- Divide out where you can ...

- Example Simplify

Using Method 2 To simplify complex fractions,

find the LCD of all of the little fractions

12x

Multiply every term by the LCD...

12x 1

12x 1

Simplify (divide out where you can )...

12x 1

12x 1

12

18

4

9

30 13

Here is a complex fraction with polynomials using

method 2 ...

- Example Simplify

LCD of all of the little fractions

x(x 2)

Multiply every term by the LCD...

x(x 2) 1

Simplify (divide out where you can )...

x(x 2) 1

x(x 2)

x

6x2 12x

4x 8

x 6x2 16x 8

The final example explores a problem that has a

fraction as one of its terms in a deep layer.

The method in question solves the equation from

the innermost fractions to the outer layer, by

finding the LCDs of that layer.

Example Simplify

Step 1. Group and expand each fractional term.

Step 2. Find the LCD of the innermost fraction.

Step 3. Simplify.

Step 4. Add fractions

Step 5. Invert and multiply.

Example (continued)

Step 6. Rewrite with LCD in both terms.

Step 7. Multiply and combine the fractions. At

the end , check to see if there are common

factors in the numerator and denominator that can

be used to reduce.

This is the final solution because there are no

common factors in the problem.