SOLUTION: Simplify the rational expression{{{4x^2-36}}} over {{{x^2+10x+21}}}

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Question 363196: Simplify the rational expression4x%5E2-36 over
x%5E2%2B10x%2B21
Answer by nyc_function(2741) About Me  (Show Source):
You can put this solution on YOUR website!
Factor the top and bottom and then reduce the fraction as needed.


4x^2 - 36 becomes (2x - 6)(2x + 6).


2x - 6 becomes 2(x - 3) and 2x + 6 becomes 2(x + 3).


The numerator becomes [4(x - 3)(x + 3)].


x^2 + 10x + 21 becomes [(x + 3)(x + 7)] = the denominator.


Our fraction now looks like this:


[4(x - 3)(x + 3)]/[(x + 3)(x + 7)]


What do you think we need to do now?


We need to cancel out common terms on the top and bottom.


I see that (x + 3) is found on the top and bottom. So, we cancel out (x + 3) on the top and bottom.

The answer is: 4(x - 3)/(x + 7).

Done!