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# Adding and Subtracting Rational Expressions:

## Presentation on theme: "Adding and Subtracting Rational Expressions:"β Presentation transcript:

Adding and Subtracting Rational Expressions:
Multiplication: Combine right across the multiplication sign. Division: Flip the second rational and multiply

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 β4 β 2 π₯ 2 β4 1 π₯+2 π₯β2 π₯ 2 β4 π₯β2 (π₯β2)(π₯+2)

Example 2: 9 5βπ₯ + 4 5βπ₯ 9+4 5βπ₯ 13 5βπ₯

Example 3: π₯ 2 π₯ β 3π₯ π₯ π₯ 3 +27 π₯ 2 β3π₯+9 π₯ 3 +27 π₯ 2 β3π₯+9 (π₯+3)( π₯ 2 β3π₯+9)

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

Example 4: 5π₯π¦ β 3π₯ 5π₯π¦ β 3 3 3π₯ β 5π¦ 5π¦ 15π₯π¦ β 15π₯π¦

Example 5: 64 π₯ 3 β π₯ (4π₯β3)(16 π₯ 2 +12π₯+9) β 2π₯ 2π₯ 2π₯ β (4π₯β3)(16 π₯ 2 +12π₯+9) (4π₯β3)(16 π₯ 2 +12π₯+9) 2π₯(4π₯β3)(16 π₯ 2 +12π₯+9) + 2π₯(4π₯β3)(16 π₯ 2 +12π₯+9)

Example 6: 15 9π₯ π₯ 15 9π₯ β 2 2 = 30 18π₯ 5 18π₯ 30 18π₯ π₯ = 35 18π₯

5 6 π₯ 2 + π₯ 4 π₯ 2 β12π₯ 5 6 π₯ 2 β 2(π₯β3) 2(π₯β3) = 10(π₯β3) 12 π₯ 2 (π₯β3)
Example 7: 5 6 π₯ 2 + π₯ 4 π₯ 2 β12π₯ 5 6 π₯ 2 β 2(π₯β3) 2(π₯β3) = 10(π₯β3) 12 π₯ 2 (π₯β3) = 3 π₯ π₯ 2 (π₯β3) β 3π₯ 3π₯ π₯ 4π₯(π₯β3)

10(π₯β3) 12 π₯ 2 (π₯β3) + 3 π₯ π₯ 2 (π₯β3) 10 π₯β3 +3 π₯ π₯ 2 (π₯β3)

2(π₯β5) 2(π₯+5)(π₯β5) β 2(π₯+5) 2(π₯+5)(π₯β5) + 4π₯ 2(π₯+5)(π₯β5)
Example 3: 1 π₯+5 β 2 2π₯β10 + 2π₯ π₯ 2 β25 1 π₯+5 β 2 2(π₯β5) + 2π₯ (π₯β5)(π₯+5) 2(π₯β5) 2(π₯+5)(π₯β5) β 2(π₯+5) 2(π₯+5)(π₯β5) + 2π₯β2 2(π₯+5)(π₯β5) 2(π₯β5) 2(π₯+5)(π₯β5) β 2(π₯+5) 2(π₯+5)(π₯β5) + 4π₯ 2(π₯+5)(π₯β5) 2 π₯β5 β2 π₯+5 +4π₯ 2(π₯+5)(π₯β5)

2π₯β10β2π₯β10+4π₯ 2(π₯+5)(π₯β5) β20+4π₯ 2(π₯+5)(π₯β5) 2 (π₯+5) 4(β5+π₯) 2(π₯+5)(π₯β5) 4(π₯β5) 2(π₯+5)(π₯β5)

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