9.5: Addition, Subtraction, and Complex Fractions Objectives: Students will be able to… Add and subtract rational expressions Simplify complex fractions

To add or subtract rational expressions you need a common denominator!!! O Example: Common Denominator…so just subtract numerators

You Try…Add or subtract

When you have unlike denominators, find the Least Common Denominator (LCD) of the rational expression. (May need to factor denominators first!!) O Rewrite each expression using the LCD O We do this with regular fractions LCD = 6

Now, lets do it with rational expressions: Factor denominators: This one needs a 2x +1 This one needs another x

Subtract. Factor Denominators: Needs an (x-3) Needs another (x+3)

You Try: Perform the indicated operation

Add or subtract.

Complex Fractions O A fraction within a fraction!! O Contains a fraction in numerator or denominator Example:

It is against the law to have a fraction within a fraction, so lets simplify: METHOD 1: Add expressions in denominator: Multiply by reciprocal, and simplify:

Method 2: Multiply numerator and denominator by LCD of both (don’t forget to distribute)

Simplify: