Reduced Speed Ahead by flickr user taberandrew

More about Rational Expressions

Operations on Rational Expressions

I Addition and Subtraction

• find a common denominator• add or subtract as required (watch your signs!)

... follow the same rules as operations on fractions (rational numbers)(although we don't

"really" subtract

anymore in high school)

SIGNS

Operations on Rational Expressions

II Mulitplication

• factor and reduce to simplest form• multiply numerators, then denominators

Remember! Any factor in

the numerator can reduce

with any factor in the

denominator

... follow the same rules as operations on fractions (rational numbers)

factor out a -1

Factor out -1

Operations on Rational Expressions

III Division• multiply the numerator by the reciprocal of the denominator (LOTS of

restrictions here!)

... follow the same rules as operations on fractions (rational numbers)

Reducing

RESTRICTIONS!

Don't upset the Math Ninja.

She's got a stick.

We "restrict" the variable (i.e. list the non-permissable values) to ensure there is no division by zero.

• restrict the denominatorsI Addition and Subtraction

RESTRICTIONS!

Don't upset the Math Ninja.

She's got a stick.

• restrict the denominatorsII Multiplication

We "restrict" the variable (i.e. list the non-permissable values) to ensure there is no division by zero.

RESTRICTIONS!

Don't upset the Math Ninja.

She's got a stick.

We "restrict" the variable (i.e. list the non-permissable values) to ensure there is no division by zero.

III Division• restrict everything except the numerator of the first fraction

Do you understand?Compare the graphs ...

Third: Reduce

Second: Restrictions?

First: Factor

First: Factor

Second: Restrictions?

Third: Reduce

Do you understand?Compare the graphs ...