Algebra Period 3 (Monday)

Simplify, Multiply, and Divide RATIONAL EXPRESSIONS 10-1, 10-2, and 10-3

Rational Expressions = Expressions in fraction format (division) with a variable in the denominator

You have already been simplifying, multiplying and dividing these throughout this year!

SIMPLIFY: 10-1

You will need to FACTOR (Chapter 6) both the numerator and denominator and "cross out" common factors in both (their quotient is 1!)
EXAMPLE: Simplify
y² + 3y + 2 =
y² - 1


(y + 2)(y + 1) =
(y - 1)(y + 1)

y + 2
y - 1

MULTIPLY: 10-2

FACTOR if possible, cross cancel if possible, multiply numerators, then denominators, simplify
EXAMPLE:
(y + 4)³[y² + 4y + 4] =
[(y + 2) ³(y² + 8y + 16)]

(y + 4) ³][ (y + 2) ² =
(y + 2) ³(y + 4) ²

y + 4
y + 2



DIVIDE: 10-3


Same as the previous example, only this time you will need to

“FLIP the SECOND” fraction,

FACTOR then
MULTIPLY!!!!!
EXAMPLE:
x + 1 ÷ x + 1 =
x² - 1 x² - 2x + 1


( x + 1) ( x2 - 2x + 1) =
(x + 1)( x - 1) (x + 1)

( x + 1)( x - 1)(x - 1) =
(x + 1)( x - 1)(x + 1)


x - 1
x + 1







Add and subtract rational expressions with LIKE DENOMINATORS: 10-4
Add and subtract with UNLIKE DENOMINATORS: 10-5
When adding with LIKE DENOMINATORS,
simply add the numerators,
simplify

When subtracting with LIKE DENOMINATORS,
CHANGE THE SIGNS
OF EACH TERM IN THE NUMERATOR AFTER THE SUBTRACTION SIGN,
THEN ADD (double check!!!)

When adding or subtracting with UNLIKE DENOMINATORS,
find the common denominator (the least common multiple of all denominators),
then use equivalent fractions to restate each numerator using the new common denominator.
EXAMPLE:
2 + x
x² - 16 x – 4

First, factor the denominators if possible



2x + x
(x + 4)(x - 4) x – 4

Find the LCM = (x + 4)(x - 4);

2x + (x + 4)(x)
(x + 4)(x - 4) (x + 4)(x - 4)


Restate both fractions with the LCM

2x + x² + 4x
(x + 4)(x - 4)


Now add the numerators

x² + 6x =
(x + 4)(x - 4)

Simplify and re-factor numerator, if possible
x(x + 6)
(x + 4)(x - 4)