Simplify each rational expression.
1. (x^2+1)/(x+1)
2. (y^2+4)/(y+2)
Check Answers:
3.(2t^2+6t+4)/(4t^2-12t-16)
Answer: (t+2)/2(t-2)
1. Simplify (x^2+1)/(x+1)
There are no common factors to cancel since (x^2+1) cannot be factorized.
There is a common factor IF the numerator had been (x^2-1)=(x+1)(x-1)
2. Simplify (y^2+4)/(y+2)
Same as #1.
Also, (y^2-4)=(y+2)(y-2)
3. Simplify (2t^2+6t+4)/(4t^2-12t-16)
(2*t^2+6*t+4)=2*(t+1)*(t+2)
(4*t^2-12*t-16)=4*(t-4)*(t+1)
By cancelling out the common factors 2 and (t+1), we get as the simplified expression
(t+2)/(2*(t-4))