Question 69270
{{{ (a+1)/(a^2+2a+1) }}} We can factor the denominator but first we will re-write the denominator:

{{{ (a+1)/(a^2+a+a+1) }}} which equals
{{{ (a+1)/(a(a+1)+(a+1)) }}} and this equals:

{{{ (a+1)/((a+1)(a+1)) }}} cancel an (a+1) in the numerator and denominator:

{{{ 1/(a+1) }}} ---------------answer

Now lets look at:

{{{a^2+2a+1}}}  This is a quadratic in standard form where:
A=1
B=2
C=1

If a quadratic can be factored and the A coefficient is 1, then the B coefficient is the sum of the factors of C.

The only factors that C has in this quadratic is 1*1 or -1*-1 and we can see that the sum of the 1*1 factor is 1+1 or 2.


Hope this helps---ptaylor