How do you combine t/(6+5t+t^2)-2/(2+3t+t^2)t6+5t+t2−22+3t+t2?

1 Answer
maganbhai P.
Mar 8, 2018

(t-3)/(t^2+4t+3)t−3t2+4t+3

Explanation:

We know that, t^3+5t+6=t^2+3t+2t+6=t(t+3)+2(t+3)=(t+3)(t+2)t3+5t+6=t2+3t+2t+6=t(t+3)+2(t+3)=(t+3)(t+2)And, t^2+3t+2=t^2+2t+t+2=t(t+2)+1(t+2)=(t+2)(t+1)t2+3t+2=t2+2t+t+2=t(t+2)+1(t+2)=(t+2)(t+1)We have, t/(t^2+5t+6)-2/(t^2+3t+2)tt2+5t+6−2t2+3t+2=t/((t+3)(t+2))-2/((t+2)(t+1))=t(t+3)(t+2)−2(t+2)(t+1)
=(t(t+1)-2(t+3))/((t+1)(t+2)(t+3))=(t^2+t-2t-6)/((t+1)(t+2)(t+3))=t(t+1)−2(t+3)(t+1)(t+2)(t+3)=t2+t−2t−6(t+1)(t+2)(t+3)=(t^2-t-6)/((t+1)(t+2)(t+3))=t2−t−6(t+1)(t+2)(t+3)
=(t^2-3t+2t-6)/((t+1)(t+2)(t+3))=((t-3)cancel((t+2)))/((t+1)cancel((t+2))(t+3))=(t-3)/((t+1)(t+3))=(t-3)/(t^2+4t+3)

Related questions
See all questions in Addition and Subtraction of Rational Expressions
Impact of this question
1476 views around the world
You can reuse this answer
Creative Commons License