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**Sums and Differences of Rational Expressions**

Objective: to add and subtract rational expressions

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**Rules for adding and subtracting fractions**

Find the least common denominator (LCD) of the fractions (that is the least common multiple of the denominators.) Express each fraction as an equivalent fraction with the LCD as the denominator Add or subtract and then simplify.

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**Examples Simplify The LCM of 5 = 5 • 1 and 15 = 5 • 3 is 15**

2. multiplying by 1 will not change a number 3.

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**Example with monomials**

Simplify The LCM of 3x2y, 12x, and 8y2 is 24x2y2 3.

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**Example with Polynomials**

Simplify Factor The LCM is (x + 3)(x – 3)(x – 1)

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**Be careful, its not done yet**

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factor

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Try These! Simplify 1. 2. 3. 4. 1. 2. 3. 4. End Show

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Try These!

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Try These!

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Try These!

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Try These!

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EXAMPLE 3 Add expressions with different denominators Find the sum 5 12x 3 9 8x28x2 5 9 8x28x2 += 9 3x 8x 2 3x + 5 2 12x 3 2 Rewrite fractions using LCD,

EXAMPLE 3 Add expressions with different denominators Find the sum 5 12x 3 9 8x28x2 5 9 8x28x2 += 9 3x 8x 2 3x + 5 2 12x 3 2 Rewrite fractions using LCD,

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