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Published byMadeleine Chambers Modified over 4 years ago

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**Adding and Subtracting Rational Expressions**

Goal Determine the LCM of polynomials Goal Add and Subtract Rational Expressions

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**What is the Least Common Multiple?**

Fractions require you to find the Least Common Multiple (LCM) in order to add and subtract them! Least Common Multiple (LCM) - smallest number or polynomial into which each of the numbers or polynomials will divide evenly. The Least Common Denominator is the LCM of the denominators.

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**Find the LCM of each set of Polynomials**

1) 12y2, 6x2 LCM = 12x2y2 2) 16ab3, 5a2b2, 20ac LCM = 80a2b3c 3) x2 – 2x, x2 - 4 LCM = x(x + 2)(x – 2) 4) x2 – x – 20, x2 + 6x + 8 LCM = (x + 4) (x – 5) (x + 2)

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**Adding Fractions - A Review**

LCD is 12. Find equivalent fractions using the LCD. Collect the numerators, keeping the LCD.

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**Remember: When adding or subtracting fractions, you need a common denominator!**

When Multiplying or Dividing Fractions, you don’t need a common Denominator

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**Steps for Adding and Subtracting Rational Expressions:**

1. Factor If possible, Cancel common factors directly over each other. Get a common denominator List out factors Multiply by 1’s Add the top (combine like terms) Re-factor and simplify if possible 4. Reduce, if possible. 5. Leave the denominators in factored form.

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**Addition and Subtraction Is the denominator the same??**

Example: Simplify Find the LCD: 6x Now, rewrite the expression using the LCD of 6x Simplify... Add the fractions... = 19 6x

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Simplify: Example 1 6(3mn2) + 8(5n) - 7(15m)

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**Adding and Subtracting with polynomials as denominators**

Simplify: Find the LCD: (x + 2)(x – 2) Rewrite the expression using the LCD of (x + 2)(x – 2) Simplify... – 5x – 22 (x + 2)(x – 2)

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**Adding and Subtracting with Binomial Denominators**

(x + 1) + 3 (x + 3) 2

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Simplify: Example 6 ** Needs a common denominator 1st! Sometimes it helps to factor the denominators to make it easier to find your LCD. LCD: 3x3(2x+1)

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Simplify: Example 7 LCD: (x+3)2(x-3)

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**Simplify: 3x (x - 1) - 2x (x + 2) (x + 3)(x + 2) (x + 3)(x - 1) LCD**

Example 9 3x (x - 1) - 2x (x + 2) (x + 3)(x + 2) (x + 3)(x - 1) LCD (x + 3)(x + 2)(x - 1) x ≠ -3, -2, 1

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**Simplify: 4x (x - 2) + 5x (x - 3) (x - 3)(x - 2) (x - 2)(x - 2) LCD**

Example 10 4x (x - 2) + 5x (x - 3) (x - 3)(x - 2) (x - 2)(x - 2) LCD (x - 3)(x - 2)(x - 2) x ≠ 3, 2

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**Simplify: (x + 3) (x - 2) - (x - 4) (x + 1) Example 11 (x - 1)(x + 1)**

LCD (x - 1)(x + 1)(x - 2) x ≠ 1, -1, 2

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