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

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Question 152263: How do you simplify a rational problem like this: 2x^2+6x+4/4x^2-12x-16, whats the answer for this problem? : How do you simplify a rational problem like this: 2x^2+6x+4/4x^2-12x-16, whats the answer for this problem?
Answer by jim_thompson5910(9376) About Me  (Show Source):
You can put this solution on YOUR website!
(2x^2+6x+4)/(4x^2-12x-16) Start with the given expression.


(2*(x+2)*(x+1))/(4x^2-12x-16) Factor 2x^2+6x+4 to get 2*(x+2)*(x+1).


(2*(x+2)*(x+1))/(2*2*(x+1)*(x-4)) Factor 4x^2-12x-16 to get 4*(x+1)*(x-4)=2*2(x+1)*(x-4).


(highlight(2)(x+2)highlight((x+1)))/(2*highlight(2)highlight((x+1))(x-4)) Highlight the common terms.


(cross(2)(x+2)cross((x+1)))/(2*cross(2)cross((x+1))(x-4)) Cancel out the common terms.


(x+2)/(2(x-4)) Simplify.


(x+2)/(2x-8) Distribute.


So (2x^2+6x+4)/(4x^2-12x-16) simplifies to (x+2)/(2x-8).


In other words, (2x^2+6x+4)/(4x^2-12x-16)=(x+2)/(2x-8) where x<>-1 or x<>4