SOLUTION: Please help me divide this equation: {{{ (a+1)/(a^2+2a+1) }}}.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me divide this equation: {{{ (a+1)/(a^2+2a+1) }}}.      Log On


   

Question 69270: Please help me divide this equation: +%28a%2B1%29%2F%28a%5E2%2B2a%2B1%29+.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
+%28a%2B1%29%2F%28a%5E2%2B2a%2B1%29+ We can factor the denominator but first we will re-write the denominator:
+%28a%2B1%29%2F%28a%5E2%2Ba%2Ba%2B1%29+ which equals
+%28a%2B1%29%2F%28a%28a%2B1%29%2B%28a%2B1%29%29+ and this equals:
+%28a%2B1%29%2F%28%28a%2B1%29%28a%2B1%29%29+ cancel an (a+1) in the numerator and denominator:
+1%2F%28a%2B1%29+ ---------------answer
Now lets look at:
a%5E2%2B2a%2B1 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