adding and subtracting rational expressions: multiplication: combine right across the multiplication...
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 simplifyingExample 1:
π₯π₯2β4
β2
π₯2β4
π₯β2π₯2β4
π₯β2(π₯β2)(π₯+2)
1π₯+2
Example 2:
95βπ₯
+45βπ₯
9+45βπ₯
135βπ₯
π₯2
π₯3+27β
3π₯π₯3+27
+ 9π₯3+27
Example 3:
π₯2β3 π₯+9π₯3+27
π₯2β3 π₯+9(π₯+3)(π₯2β3π₯+9)
ADDING & SUBTRACTING UNLIKE DENOMINATORS
1. Factor the denominators and determine the LCD
2. Rewrite each fraction over the LCD
3. Add or subtract the numerators by combining like terms and put over the denominator
4. Follow the steps for simplifying
http://www.khanacademy.org/math/algebra/rational-expressions/rational_expressions/v/adding-and-subtracting-rational-expressions
β5π₯π¦
β3π₯β
33 β
5 π¦5 π¦
β15π₯π¦
β β15π₯π¦
Example 4:
β5π₯π¦
β β3π₯
Example 5: β64 π₯3β27
+ β2π₯
β(4 π₯β3)(16 π₯2+12 π₯+9)β2π₯
β2 π₯2 π₯
β(4 π₯β3)(16 π₯2+12π₯+9)(4 π₯β3)(16 π₯2+12π₯+9)
β2π₯ (4 π₯β3)(16 π₯2+12 π₯+9)
+ β2π₯ (4 π₯β3)(16 π₯2+12 π₯+9)
Example 6:
159π₯
+518 π₯
159π₯
518π₯
β22=3018 π₯
3018π₯
+518 π₯
=3518 π₯
5
6 π₯2β2 (π₯β3)2 (π₯β3)π₯
4 π₯ (π₯β3)β3 π₯3 π₯
Example 7:
5
6 π₯2+
π₯4 π₯2β12π₯
ΒΏ10 (π₯β3)12π₯2(π₯β3)
ΒΏ 3 π₯2
12π₯2(π₯β3)
10(π₯β3)12π₯2(π₯β3)
+ 3 π₯2
12π₯2(π₯β3)
10 (π₯β3 )+3π₯2
12π₯2(π₯β3)
1π₯+5
β2
2π₯β10+2 π₯
π₯2β25
Example 3:
1π₯+5
β2
2(π₯β5)+
2π₯(π₯β5)(π₯+5)
2(π₯β5)2(π₯+5)(π₯β5)
β2(π₯+5)
2(π₯+5)(π₯β5)+2 π₯ β2
2(π₯+5)(π₯β5)