Questions on Algebra: Polynomials, rational expressions and equations answered by real tutors!

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Question 152484: How do you DIVIDE this rational expression:x^2+13x+12/x+2(divided by)x+1. : How do you DIVIDE this rational expression:x^2+13x+12/x+2(divided by)x+1.
Answer by jim_thompson5910(9376) About Me  (Show Source):
You can put this solution on YOUR website!
((x^2+13x+12)/(x+2))/(x+1) Start with the given expression.


((x^2+13x+12)/(x+2))/((x+1)/(1)) Rewrite x+1 as (x+1)/(1)


((x^2+13x+12)/(x+2))((1)/(x+1)) Multiply the first fraction (x^2+13x+12)/(x+2) by the reciprocal of the second fraction (x+1)/(1).


(((x+12)(x+1))/(x+2))((1)/(x+1)) Factor x^2+13x+12 to get (x+12)(x+1).


((x+12)(x+1))/((x+2)(x+1)) Combine the fractions.


((x+12)highlight((x+1)))/((x+2)highlight((x+1))) Highlight the common terms.


((x+12)cross((x+1)))/((x+2)cross((x+1))) Cancel out the common terms.


(x+12)/(x+2) Simplify.


So ((x^2+13x+12)/(x+2))/(x+1) simplifies to (x+12)/(x+2).


In other words, ((x^2+13x+12)/(x+2))/(x+1)=(x+12)/(x+2) where x<>-1 or x<>-2