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How do you find the least common denominator for rational expressions?

Answer 1

Eli Assouline

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.

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Answer 2

Savannah Anderson

To find the least common denominator for rational expressions, follow these steps:

Factor the denominators of all the rational expressions.
Identify the common factors and the unique factors in each denominator.
Take the product of all the unique factors, including the common factors raised to their highest power.
This product will be the least common denominator for the rational expressions.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.