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