SOLUTION: 25-b^2/b^2+12b+35

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Question 189549: 25-b^2/b^2+12b+35
Found 2 solutions by jim_thompson5910, Earlsdon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%2825-b%5E2%29%2F%28b%5E2%2B12b%2B35%29 Start with the given expression.


%28-%28b-5%29%28b%2B5%29%29%2F%28b%5E2%2B12b%2B35%29 Factor 25-b%5E2 to get -%28b-5%29%28b%2B5%29.


%28-%28b-5%29%28b%2B5%29%29%2F%28%28b%2B7%29%28b%2B5%29%29 Factor b%5E2%2B12b%2B35 to get %28b%2B7%29%28b%2B5%29.


-%28%28b-5%29highlight%28%28b%2B5%29%29%29%2F%28%28b%2B7%29highlight%28%28b%2B5%29%29%29 Highlight the common terms.


-%28%28b-5%29cross%28%28b%2B5%29%29%29%2F%28%28b%2B7%29cross%28%28b%2B5%29%29%29 Cancel out the common terms.


-%28b-5%29%2F%28b%2B7%29 Simplify.


So %2825-b%5E2%29%2F%28b%5E2%2B12b%2B35%29 simplifies to -%28b-5%29%2F%28b%2B7%29.


In other words, %2825-b%5E2%29%2F%28b%5E2%2B12b%2B35%29=-%28b-5%29%2F%28b%2B7%29 where b%3C%3E-7 or b%3C%3E-5

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify:
%2825-b%5E2%29%2F%28b%5E2%2B12b%2B35%29 Rewrite the numerator as a negative binomial:
%28-%28b%5E2-25%29%29%2F%28b%5E2%2B12b%2B35%29 Now factor both the numerator and the denominator.
-%28b-5%29cross%28%28b%2B5%29%29%2F%28%28b%2B7%29cross%28%28b%2B5%29%29%29 Finally, cancel the indicated factors.
highlight%28-%28b-5%29%2F%28b%2B7%29%29