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8-2 Adding and Subtracting Rational Expressions Determine the least common denominator. Add and Subtract rational expressions.

Adding and subtracting rational expressions is similar to adding and subtracting fractions. YOU NEED COMMON DENOMINATORS. Least common multiples of denominators can be found by comparing prime factorizations. If two or more polynomials are factored, their least common multiple will include each factor with an exponent indicating the maximum number of times that factor appears in one of the polynomials.

Find the LCM of each set of polynomials

To add and subtract rational expressions: Make sure the expressions have common denominators. If not, find the LCM of the given denominators and rewrite each rational expression as an equivalent expression having the LCM as its denominator. The sum (or difference) of rational expressions with common denominators is equal to an expression in which the denominator is the common denominator and the numerator is the sum (or difference) of the numerators. -KEEP THE BOTTOM, ADD (or subtract) THE TOPS!!

Equivalent Expressions When rational expressions are given the same denominators in preparation for addition or subtraction, they are equivalent to the original expressions. Multiplying a rational expression by a form of 1 such as  or     does not change the value of the expression.

SIMPLIFY THE EXPRESSION

SIMPLIFY THE EXPRESSION Be especially careful of signs with subtraction!

SIMPLIFY THE EXPRESSION

SIMPLIFY THE EXPRESSION

When working with complex fractions, first get one fraction in the numerator, then get one fraction in the denominator.

SIMPLIFY THE EXPRESSION

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