SOLUTION: Simplify the complex rational expression 3 + 12/x _________ 1 - 16/x^2

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Question 191829This question is from textbook Introductory Algebra for College Students
: Simplify the complex rational expression
3 + 12/x
_________
1 - 16/x^2 This question is from textbook Introductory Algebra for College Students

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify the complex rational expression
3 + 12/x
_________
1 - 16/x^2
-----------------
= (3x+12)/x // ((x^2-16)/x^2
The quickest and least error-prone way to do these it make a new fraction by multiplying the "outside" terms, in this case (3x+12) and x^2 (NUM) and the "inside" terms, x*(x^2-16).
--> x^2*(3x+12)/(x*(x^2-16))
= x*3*(x+4)/(x+4)*(x-4)
= 3x/(x-4)