9.4 multiplying & dividing rational expressions. simplifying rational expressions if the top and...
TRANSCRIPT
9.4 Multiplying & Dividing Rational Expressions
Simplifying Rational Expressions
• If the top and bottom have a common term, they can cancel out.
bc
ac
b
a
Example #1Simplify the Expression
• Do you notice anything similar on top and bottom?
y
x
3
3
y
x
Example #2 Simplify the Expression
• Notice how the top and bottom both have “(x – 2)”. They cancel out.
)3)(2(
)2)(3(
xx
xx
3
3
x
x
• Also, notice the top has “(x + 3)” and the bottom has “(x – 3),” which are different. They DO NOT cancel out.
Example #3 Simplify the Expression
• Notice “x2 – 4” can be factored to (x + 2)(x – 2)
)3)(2(
42
xx
x
3
2
x
x
• Again, the top has “(x + 2)” and the bottom has “(x – 3),” so they DO NOT cancel out.
)3)(2(
)2)(2(
xx
xx
• Notice how the top and bottom both have “(x – 2)”. They cancel out.
Example #4 Multiply
• How do you multiply fractions?
5
1
1
2
x
x
x
x
Straight across
• We don’t even want to multiply, we just want to cancel.
)5)(1(
)1)(2(
xx
xx
• Is there anything we can cancel?
5
2
x
x
Example #5 Divide
• Dividing is the same as multiplying by the reciprocal.
7
2
3
2
x
x
x
x
2
7
3
2
x
x
x
x
• Again, we don’t even want to multiply.
3
7
x
x
Practice #1Simplify the expression
)6)(3(
)1)(6(
xx
xx
1
3
x
x
Practice #2Simplify the expression
1
652
2
x
xx
6
1
x
x
Practice #3Multiply
1
6
2
232
22
x
xx
x
xx
2 6
1
x x
x
3 2
1
x x
x
or
Practice #4Divide
16
168
4
822
22
x
xx
x
xx
2x
2 2
2
2 8 16
4 8 16
x x x
x x x
Practice #5Divide
63
4
3
5 22
x
x
x
xx
5
2
x
x
2
2
5 3 6
3 4
x x x
x x