SOLUTION: Simplify (-x^2-4x+21)/(3-x)

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Question 633603: Simplify
(-x^2-4x+21)/(3-x)
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
%28-x%5E2-4x%2B21%29%2F%283-x%29

Quadratics are difficult to factor if the leading term is negative,
To make the x² term positive, let's multiply by %28%28-1%29%2F%28-1%29%29

%28%28-1%29%2F%28-1%29%29·%28%28-x%5E2-4x%2B21%29%2F%283-x%29%29 =

%28-1%28-x%5E2-4x%2B21%29%29%2F%28-1%283-x%29%29

%28x%5E2%2B4x-21%29%2F%28-3%2Bx%29

Write the denominator in descending order:

%28x%5E2%2B4x-21%29%2F%28x-3%29

Factor the numerator

%28%28x%2B7%29%28x-3%29%29%2F%28x-3%29

Cancel the (x-3)'s

%28%28x%2B7%29%28cross%28x-3%29%29%29%2F%28cross%28x-3%29%29

x+7

Edwin