Addition and Subtraction of Rational Expressions
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Key Questions

#A/B + C/D = (AD + BC)/(BD)# and
#A/B  C/D = (AD  BC)/(BD)# 
You can keep the same denominator and add or subtract the numerators.
#a/c+b/c={a+b}/c# and#a/cb/c={ab}/c#
I hope that this was helpful.

The least common denominator is the least common multiple of denominators.
Example
Find the least common denominator to compute:#1/3+1/41/6# Let us observe:
Multiples of
#3# :#3,6,9# , 12,#15,...#
Multiples of#4# :#4,8# ,12,#16,...#
Multiples of#6# :#6# ,12,#18,...# ,So, the least common multiple of
#3# ,#4# , and#6# is#12# .Hence,
#1/3+1/41/6=4/12+3/122/6={4+32}/12=5/12#
...
I hope that this was helpful. 
Imagine your fractions are
#a/b# and#c/d# .Obviously
#a/b=(ad)/(bd)# and#c/d=(cb)/(db)# ,so
#a/b+c/d=(ad)/(bd)+(cb)/(db)=(ad+cb)/(bd)# .Also,
#a/bc/d=(ad)/(bd)(cb)/(db)=(adcb)/(bd)# .
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Videos on topic View all (3)
Rational Equations and Functions

1Inverse Variation Models

2Graphs of Rational Functions

3Division of Polynomials

4Excluded Values for Rational Expressions

5Multiplication of Rational Expressions

6Division of Rational Expressions

7Addition and Subtraction of Rational Expressions

8Rational Equations Using Proportions

9Clearing Denominators in Rational Equations

10Surveys and Samples