# Adding and Subtracting Rational Expressions:

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

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

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)

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)