Algebra (Period 1)

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