SOLUTION: Please simplify the expression if possible: x^2 + 10x + 24 / x^2 - 16

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Question 723989: Please simplify the expression if possible: x^2 + 10x + 24 / x^2 - 16
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

%28x%5E2+%2B+10x+%2B+24%29+%2F+%28x%5E2+-+16%29
%28x%5E2+%2B+10x+%2B+24%29+%2F+%28x%5E2+-+4%5E2%29

factor completely %28x%5E2+%2B+10x+%2B+24%29 and %28x%5E2+-+4%5E2%29

x%5E2+%2B+10x+%2B+24.......substitute 10x with 4x+%2B6x

x%5E2+%2B+4x+%2B6x+%2B+24...group

%28x%5E2+%2B+4x%29+%2B%286x+%2B+24%29

x%28x+%2B+4%29+%2B6%28x+%2B+4%29

%28x+%2B6%29%28x+%2B+4%29
and
%28x%5E2+-+4%5E2%29...use the rule a%5E2-b%5E2=%28a-b%29%28a%2Bb%29
%28x+-+4%29%28x+%2B+4%29

now plug it in your expression

%28%28x+%2B6%29%28x+%2B+4%29%29+%2F+%28%28x+-+4%29%28x+%2B+4%29%29...simplify

%28%28x+%2B6%29cross%28%28x+%2B+4%29%29%29+%2F+%28%28x+-+4%29cross%28%28x+%2B+4%29%29%29

%28x+%2B6%29+%2F+%28x+-+4%29