Adding and subtracting rational expressions:

1
Adding and subtracting rational expressions

• To add or subtract rational expressions use the
  addition property

Taken from http//podcasts.shelbyed.k12.al.us/scle
mons/files/2011/05/add-subtraction-rationals.ppt1
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If the expressions have the same (common)
denominator, add or subtract the numerators, keep
the same denominator, and simplify the result.
Taken from http//podcasts.shelbyed.k12.al.us/scle
mons/files/2011/05/add-subtraction-rationals.ppt1
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Do the operations and simplify the result
Taken from http//podcasts.shelbyed.k12.al.us/scle
mons/files/2011/05/add-subtraction-rationals.ppt1
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Taken from http//podcasts.shelbyed.k12.al.us/scle
mons/files/2011/05/add-subtraction-rationals.ppt1
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Taken from http//podcasts.shelbyed.k12.al.us/scle
mons/files/2011/05/add-subtraction-rationals.ppt1
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Taken from http//podcasts.shelbyed.k12.al.us/scle
mons/files/2011/05/add-subtraction-rationals.ppt1
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Taken from http//podcasts.shelbyed.k12.al.us/scle
mons/files/2011/05/add-subtraction-rationals.ppt1
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To add or subtract fractions with different
denominators find the least common denominator
(LCD), change each fraction so that it has that
denominator then add or subtract
Simply stated, the LCD is the least number
(expression) that all denominators will divide
into evenly.
Taken from http//podcasts.shelbyed.k12.al.us/scle
mons/files/2011/05/add-subtraction-rationals.ppt1
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To find the LCD

• factor each denominator
• write the different factors
• give each factor the highest power to which it
  occurs
• multiply the results

Taken from http//podcasts.shelbyed.k12.al.us/scle
mons/files/2011/05/add-subtraction-rationals.ppt1
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Find the LCD for y²-16 and y²-8y16

• Factor each
• write each factor
• give each highest exponent
• multiply results

• (y4)(y-4) and (y-4)²
• (y4)(y-4)
• (y4)(y-4)²
• (y4)(y-4)²

Taken from http//podcasts.shelbyed.k12.al.us/scle
mons/files/2011/05/add-subtraction-rationals.ppt1
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Add

• LCD
• change each fraction to LCD
• add/subtract
• simplify

Taken from http//podcasts.shelbyed.k12.al.us/scle
mons/files/2011/05/add-subtraction-rationals.ppt1
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Add

• LCD
• change each fraction to LCD
• add/subtract
• simplify

Taken from http//podcasts.shelbyed.k12.al.us/scle
mons/files/2011/05/add-subtraction-rationals.ppt1
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Add

• LCD
• change each fraction to LCD
• add/subtract
• simplify

(Top isnt factorable)
Taken from http//podcasts.shelbyed.k12.al.us/scle
mons/files/2011/05/add-subtraction-rationals.ppt1
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If the denominators have opposite factors, then
change one of them using the 3 signs of a
fraction rule.
Taken from http//podcasts.shelbyed.k12.al.us/scle
mons/files/2011/05/add-subtraction-rationals.ppt1
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Taken from http//podcasts.shelbyed.k12.al.us/scle
mons/files/2011/05/add-subtraction-rationals.ppt1
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1)
2)
3)
4)
Taken from http//podcasts.shelbyed.k12.al.us/scle
mons/files/2011/05/add-subtraction-rationals.ppt1
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Taken from http//podcasts.shelbyed.k12.al.us/scle
mons/files/2011/05/add-subtraction-rationals.ppt1
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(x3) (x-2) (x3) (x-5)
(x-5) (x-2)
Taken from http//podcasts.shelbyed.k12.al.us/scle
mons/files/2011/05/add-subtraction-rationals.ppt1
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(y 2) (y2)
-(y-2)(y2)
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(x-1) (x-1)(x1)
(x1)(x1)
LCM (x-1)(x1)(x1)
Taken from http//podcasts.shelbyed.k12.al.us/scle
mons/files/2011/05/add-subtraction-rationals.ppt1