Subtracting Rational Expressions (Same Denominator)
Subtract. Write the answer in lowest terms.Subtract numerators.
Keep the same denominator.Distributive property= Combine like terms.m- 3
m- 1=
2 m-m- 3
m- 1=
2 m- 1 m+ 32
m- 12 m
m- 1-
m+ 3
m- 1EXAMPLE 6444 CHAPTER 7 Rational Expressions and Applications
CAUTION Sign errors often occur in subtraction problems like the one in
Example 6.The numerator of the fraction being subtracted must be treated as a sin-
gle quantity. Be sure to use parentheses after the subtraction symbol.NOW TRY
EXERCISE 6
Subtract. Write the answer in
lowest terms.
2 x
x+ 5x+ 1
x+ 5NOW TRY ANSWERS
6.xx-+^15
Use parentheses
around the numerator
of the subtrahend.Be careful
with signs.NOW TRYSubtracting Rational Expressions (Different Denominators)
Subtract. Write the answer in lowest terms.The LCD isWrite each expression with the LCD.Subtract numerators.
Keep the same denominator.Distributive property,or Combine like terms.
Factor the numerator.61 x+ 12
x 1 x- 22=
6 x+ 6
x 1 x- 22=
9 x- 3 x+ 6
x 1 x- 22=
9 x- 31 x- 22
x 1 x- 22=
9 x
x 1 x- 22-
31 x- 22
x 1 x- 22x 1 x- 22.9
x- 2-
3
xNOW TRY EXAMPLE 7
EXERCISE 7
Subtract. Write the answer in
lowest terms.
6
y- 62
y- 41 y+ 32
y 1 y- 62
Be careful
with signs.NOW TRYNOTE We factored the final numerator in Example 7to get. The fundamental
property does not apply, however since there are no common factors to divide out. The
answer is in lowest terms.Subtracting Rational Expressions (Denominators Are Opposites)
Subtract. Write the answer in lowest terms.
3 x
x- 5-
2 x- 25
5 - xEXAMPLE 861 x + 12
x 1 x- 22The denominators are opposites. We choose
x- 5 as the common denominator.Multiply by to get a
common denominator.= 15 - x 21 - 12 =- 5 +x=x- 53 x
x- 5-
- 2 x+ 25
x- 5- 1
- 1
2 x- 25
=^3 x^5 - x
x- 5
-
12 x- 2521 - 12
15 - x 21 - 12http://www.ebook777.com
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