SOLUTION: Hello........Can someone help me with this one? Reduce the given expression to lowest terms. 3x^(2)+7x+2/4x^(2)-16

Algebra ->  Expressions-with-variables -> SOLUTION: Hello........Can someone help me with this one? Reduce the given expression to lowest terms. 3x^(2)+7x+2/4x^(2)-16      Log On


   

Question 205391: Hello........Can someone help me with this one?
Reduce the given expression to lowest terms.
3x^(2)+7x+2/4x^(2)-16
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%283x%5E2%2B7x%2B2%29%2F%284x%5E2-16%29 Start with the given expression.


%28%28x%2B2%29%283x%2B1%29%29%2F%284x%5E2-16%29 Factor 3x%5E2%2B7x%2B2 to get %28x%2B2%29%283x%2B1%29.


%28%28x%2B2%29%283x%2B1%29%29%2F%284%28x-2%29%28x%2B2%29%29 Factor 4x%5E2-16 to get 4%28x-2%29%28x%2B2%29.


%28highlight%28%28x%2B2%29%29%283x%2B1%29%29%2F%284%28x-2%29highlight%28%28x%2B2%29%29%29 Highlight the common terms.


%28cross%28%28x%2B2%29%29%283x%2B1%29%29%2F%284%28x-2%29cross%28%28x%2B2%29%29%29 Cancel out the common terms.


%283x%2B1%29%2F%284%28x-2%29%29 Simplify.


%283x%2B1%29%2F%284x-8%29 Distribute


So %283x%5E2%2B7x%2B2%29%2F%284x%5E2-16%29 simplifies to %283x%2B1%29%2F%284x-8%29.


In other words, %283x%5E2%2B7x%2B2%29%2F%284x%5E2-16%29=%283x%2B1%29%2F%284x-8%29