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Adding/Subtracting Fractions with Variables and Exponents Help

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By — McGraw-Hill Professional
Updated on Sep 26, 2011

Adding/Subtracting Fractions with Variables and Exponents

When adding fractions with variables in one or more denominators, the LCD will have each variable (or algebraic expression) to its highest power as a factor. For example, the LCD for Adding/Subtracting Fractions is x 2 y 3 .

Examples

Adding/Subtracting Fractions Examples

Find practice problems and solutions at Adding/Subtracting Fractions: Practice Problems - Set 1.

Exponent Properties 5 & 6 - Adding/Subtracting Fractions with Variables and Negative Exponents

Property 5 - Negative Exponents

 Adding/Subtracting Fractions Solutions

This property says that a –1 is the reciprocal of a . In other words, a –1 means “invert a .”

(Review Exponent Properties 1-4)

Examples

Adding/Subtracting Fractions Examples 2

Property 6 - Negative Exponents Other than One

Adding/Subtracting Fractions Examples 3

This is a combination of Properties 3 and 5: Adding/Subtracting Fractions Examples 4 .

Examples

Adding/Subtracting Fractions Examples 5

Often a combination of exponent properties is needed. In the following examples the goal is to rewrite the expression without using a negative exponent.

Examples

Adding/Subtracting Fractions Examples 6

Find practice problems and solutions at Adding/Subtracting Fractions: Practice Problems - Set 2.

Exponent Properties 7 & 8 - Adding/Subtracting Fractions with Variables and Exponents with Products and Quotients

In expressions such as (2 x ) –1 the exponent “–1” applies to 2 x , but in 2 x –1 the exponent “–1” applies only to x :

Adding/Subtracting Fractions Solutions 2

Property 7 - Power of Products

( ab) n = a n b n

By Property 7 we can take a product then the power or take the powers then the product.

Examples

Adding/Subtracting Fractions Examples 7

It is not true that (a + b) n = a n + b n . This mistake is very common.

Property 8 - Property of Quotients

Adding/Subtracting Fractions Examples 8

Property 8 says that we can take the quotient first then the power or each power followed by the quotient.

Examples

Adding/Subtracting Fractions Examples 9

This example will be used for the rest of the examples and practice problems.

Adding/Subtracting Fractions Examples 10

This expression can be simplified more quickly using Property 8 and Property 3.  (Review Exponent Properties 1-4)

Adding/Subtracting Fractions Examples 11

Find practice problems and solutions at Adding/Subtracting Fractions Practice Problems - Set 3.

More practice problems for this concept can be found at: Exponents and Roots Practice Test.

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