Simplifying Rational Expressions Module 8 MAT0028 1) Values that make a Rational Expression Undefined: EX) What makes the rational expression undefined f ( x) 
x6
x  x6
2
2) Fundamental Principle of Fractions ∙
∙
3) Remember: a) b) c) 7‐a = Write each rational expression in lowest terms. y 2  5 y  14
EX1) 2
y  y2
EX2) 7 x  21
63  21x
4) Multiplying Rational Expressions ∙
Dividing Rational Expressions ∙ Write each rational expression in lowest terms x 3
x 2  25

EX1) 2
x  2 x  15 x 2  3x  40
k2  4 2  k
EX2) 2 
3k
11k
5) Sum/ Difference of Rational Expressions 
Idea: get common denominator, +/‐ numerator, keep denominator a) Factor Each Denominator first Find LCD = (product of each distinct factor the max # of times it appears in single denominator) b) Build each Fraction so Den = LCD, Simplify each numerator separately c) Combine since denominators match (LCD) (Keep Den= LCD, add numerator) d) Simplify if possible (once it is single fraction – check does numerator factor) State the Least Common Denominator: 1)
1
1
,
3 5
8 x y 12 x5 yz 2
2) 1
1
,
3
20 x( y  3) 30 x ( y  3)2
LCD = _____________ LCD = ______________ 3) 1
1
, 2
x  4 x  7 x  10
2
LCD = _____________ Add or subtract as indicated. Write all answers in lowest terms. 1. 3x  1
2x  7
3
1
3
8
5
2
 2


 2
2. 3. 4. 2
x  5x  6 x  5x  6
2 x x2
10 x  15 12 x  18
x  6x  9 x  4x  3
2