Addition and Subtraction of Rational Expressions

Key Questions

How do you add or subtract rational expressions with the same denominator?

You can keep the same denominator and add or subtract the numerators.

#a/c+b/c={a+b}/c# and #a/c-b/c={a-b}/c#

I hope that this was helpful.

Wataru · 1 · Oct 26 2014
How do you find the least common denominator for rational expressions?

The least common denominator is the least common multiple of denominators.

Example
Find the least common denominator to compute:

#1/3+1/4-1/6#

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+1/4-1/6=4/12+3/12-2/6={4+3-2}/12=5/12#
...
I hope that this was helpful.

Wataru · 1 · Nov 2 2014
How do you add or subtract rational expressions with unlike denominator?

You need to put each term over a common denominator by multiplying each term by the appropriate form of #1# or #n/n#

smendyka · 1 · Jul 25 2018
What is Addition and Subtraction of Rational Expressions?

#A/B + C/D = (AD + BC)/(BD)#

and

#A/B - C/D = (AD - BC)/(BD)#

vince · 1 · Feb 24 2015