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**Adding and Subtracting Rational Expressions:**

Multiplication: Combine right across the multiplication sign. Division: Flip the second rational and multiply

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**Adding & Subtracting like Denominators**

1. Add or subtract the numerators by combining like terms and put over the denominator 2. Follow the steps for simplifying Example 1: π₯ π₯ 2 β4 β 2 π₯ 2 β4 1 π₯+2 π₯β2 π₯ 2 β4 π₯β2 (π₯β2)(π₯+2)

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Example 2: 9 5βπ₯ + 4 5βπ₯ 9+4 5βπ₯ 13 5βπ₯

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Example 3: π₯ 2 π₯ β 3π₯ π₯ π₯ 3 +27 π₯ 2 β3π₯+9 π₯ 3 +27 π₯ 2 β3π₯+9 (π₯+3)( π₯ 2 β3π₯+9)

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**Adding & Subtracting UNLIKE Denominators**

Factor the denominators and determine the LCD Rewrite each fraction over the LCD Add or subtract the numerators by combining like terms and put over the denominator Follow the steps for simplifying

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Example 4: 5π₯π¦ β 3π₯ 5π₯π¦ β 3 3 3π₯ β 5π¦ 5π¦ 15π₯π¦ β 15π₯π¦

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Example 5: 64 π₯ 3 β π₯ (4π₯β3)(16 π₯ 2 +12π₯+9) β 2π₯ 2π₯ 2π₯ β (4π₯β3)(16 π₯ 2 +12π₯+9) (4π₯β3)(16 π₯ 2 +12π₯+9) 2π₯(4π₯β3)(16 π₯ 2 +12π₯+9) + 2π₯(4π₯β3)(16 π₯ 2 +12π₯+9)

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Example 6: 15 9π₯ π₯ 15 9π₯ β 2 2 = 30 18π₯ 5 18π₯ 30 18π₯ π₯ = 35 18π₯

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**5 6 π₯ 2 + π₯ 4 π₯ 2 β12π₯ 5 6 π₯ 2 β 2(π₯β3) 2(π₯β3) = 10(π₯β3) 12 π₯ 2 (π₯β3)**

Example 7: 5 6 π₯ 2 + π₯ 4 π₯ 2 β12π₯ 5 6 π₯ 2 β 2(π₯β3) 2(π₯β3) = 10(π₯β3) 12 π₯ 2 (π₯β3) = 3 π₯ π₯ 2 (π₯β3) β 3π₯ 3π₯ π₯ 4π₯(π₯β3)

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10(π₯β3) 12 π₯ 2 (π₯β3) + 3 π₯ π₯ 2 (π₯β3) 10 π₯β3 +3 π₯ π₯ 2 (π₯β3)

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**2(π₯β5) 2(π₯+5)(π₯β5) β 2(π₯+5) 2(π₯+5)(π₯β5) + 4π₯ 2(π₯+5)(π₯β5)**

Example 3: 1 π₯+5 β 2 2π₯β10 + 2π₯ π₯ 2 β25 1 π₯+5 β 2 2(π₯β5) + 2π₯ (π₯β5)(π₯+5) 2(π₯β5) 2(π₯+5)(π₯β5) β 2(π₯+5) 2(π₯+5)(π₯β5) + 2π₯β2 2(π₯+5)(π₯β5) 2(π₯β5) 2(π₯+5)(π₯β5) β 2(π₯+5) 2(π₯+5)(π₯β5) + 4π₯ 2(π₯+5)(π₯β5) 2 π₯β5 β2 π₯+5 +4π₯ 2(π₯+5)(π₯β5)

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2π₯β10β2π₯β10+4π₯ 2(π₯+5)(π₯β5) β20+4π₯ 2(π₯+5)(π₯β5) 2 (π₯+5) 4(β5+π₯) 2(π₯+5)(π₯β5) 4(π₯β5) 2(π₯+5)(π₯β5)

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