Aim: How do we multiply and divide rational expressions?
To multiply or divide a rational expression, you have to factor out any expression that can be factored and then multiply or divide.
Example
3x-9/x-2*x^2-2x/x-3
1) Factor 3x-9
3(x-3)/x-2
2) Factor x^2-2x
x(x-2)/x-3
4) Divide x-3/x-3 and x-2/x-2
*You can cross them out as they both equal to 1
5) Multiply the remaining 3 and x on the numerator
3x
Excluded Value:
Find any problem that would make the denominator equal to zero.
x-2=0 x-3=0
+2 +2 +3 +3
x=2 x=3
x canont be eqaul to 2 or 3
Example
(2b^2-12b/b+5)/(b-6/b+5)
1) Keep the the fraction on the left but change the division sign and fraction
on the right
(2b^2-12b/b+5)*(b+5/b-6)
2) Factor 2b^2- 12b
2b(b-6)
3) Divide b-6/b-6 and b+5/b+5
* Cross them out because they equal to one
4) This only leaves 2b on the numerator
2b
Excluded value:
b+5=0 b-6=0
-5 -5 +6 +6
b= 5 b=6
b cannot be equal to 5 or 6.
* Note you also use the denominator you get after flipping
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