Warm Up #13

1 (6x3 + 12x2 – 18x) 3x

2 (4x2 + 9x +2) (x+2)

3 (x3 + 216) (x + 6)

Warm Up #13:

1 (6x3 + 12x2 – 18x) 3x

2 (4x2 + 9x +2) (x+2)

3 (x3 + 216) (x + 6)x2 – 6x +36

4x + 1

2x2 + 4x - 6

Complex Rational Expressions

3

21x

13

243

xx

x

yx

x

x

23

281

Fractions inside of fractions are a NO - NO

And must be simplified.

To simplifyComplex Rational Expressions

• Multiply the numerator and denominator by a fraction equivalent to “1”

• The fraction should contain the factors of all denominators in the expression

8

243

x

x

88

xx46

Complex Rational Expressions• Multiply the numerator and denominator

by a fraction equivalent to “1”• The fraction should contain the factors

of all denominators in the expression

211

11

x

x

2

2

xx

12

2

xxx

111

xx

xx

1xx

Steps

1. Find the LCD of the numerator and denominator

2. Multiply the complex rational expression by the LCD/LCD (so its equivalent to multiplying by 1)

3. Simplify (factor and cross out common factors)

xx

1

5xx

21

32xx

35x

8/5

yy

2

11

yy

1

1 1y

y y

11y

Short Cut

• If there are 2 terms or more on either the numerator or denominator you must multiply by the LCD/LCD

• However, if there is only 1 term on the numerator and 1 term on the denominator then you can divide fractions (which means multiply by the reciprocal)

2

1223

xxxx

123xx

21223

xx

xx

xx

xx2

1223

Assignment:

Page 4702-27 odd