simplifying rational expressions: addition and subtraction
TRANSCRIPT
Simplifying Rational Expressions: Addition and Subtraction
Adding and Subtracting Fractions
2 13 5 7 3
4 105 32 1
3 5 5 3 7 5 3 24 5 10 2 35 620 20
Add the Numerators
Least Common
Denominator (if you can
find it)Common
Denominator
Remember to Simplify if Possible!
Addition: Subtraction:
10 315 151315
2920
Subtract the Numerators
Add/Subtract Rational Expressions
2 2
2 1 4
2 15 2 15
x x
x x x x
2
2 1 4
2 15
x x
x x
2
2 1 4
2 15
x x
x x
2
5
2 15
x
x x
Simplify: Same denominator! Half the work is done!
CAREFUL with subtraction!
Combine Like Terms
5
5 3
x
x x
1
3x
Make sure it can’t be simplified more
Add/Subtract Rational Expressions
2
7 11
2x x
2
7 11 2
22x x
x
x
2 2
7 22
2 2
x
x x
2
7 22
2
x
x
Simplify: Find a Common Denominator
Combine Like Terms
Add/Subtract Rational Expressions
3 5
3 2x x
23 5
3 2
3
2 3
x x
x xx x
3 6 5 15
3 2 2 3
x x
x x x x
3 6 5 15
3 2
x x
x x
Simplify: Find a common denominator
Distribute numerators but leave the
denominators factored
CAREFUL with subtraction
3 6 5 15
3 2
x x
x x
2 21
3 2
x
x x
Combine like Terms
Add/Subtract Rational Expressions
2
8 5
6 2 3 1
x
x x x
8 5
2 3 1 3 1
x
x x x
2 4 5
2 3 1 3 1
x
x x x
4 5
3 1 3 1x x
Simplify: Factor to find a Smaller Common Denominator
4 5
3 1x
1
3 1x
Make sure it can’t be simplified beforehand
Add/Subtract Rational Expressions
2
2
16 3 12
x x
x x
2
4 4 3 4
x x
x x x
2
4 4
43
3 43 4
x x
x x
x
xx
23 6 4
3 4 4 3 4 4
x x x
x x x x
Simplify: Factor to find a Smaller Common Denominator
23 6 4
3 4 4
x x x
x x
2 6
3 4 4
x x
x x
3 2
3 4 4
x x
x x
Make sure it can’t be
simplified more