SOLUTION: please help with step by step 21x^2-49x-42 over 4x^2-28x+48 divided by 21x+14 over 8x^2-32x

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Question 200970: please help with step by step 21x^2-49x-42 over 4x^2-28x+48 divided by 21x+14 over 8x^2-32x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%2821x%5E2-49x-42%29%2F%284x%5E2-28x%2B48%29%29%2F%28%2821x%2B14%29%2F%288x%5E2-32x%29%29 Start with the given expression.


%28%2821x%5E2-49x-42%29%2F%284x%5E2-28x%2B48%29%29%28%288x%5E2-32x%29%2F%2821x%2B14%29%29 Multiply the first fraction %2821x%5E2-49x-42%29%2F%284x%5E2-28x%2B48%29 by the reciprocal of the second fraction %2821x%2B14%29%2F%288x%5E2-32x%29.


Factor 21x%5E2-49x-42 to get 7%283x%2B2%29%28x-3%29.


Factor 4x%5E2-28x%2B48 to get 4%28x-3%29%28x-4%29.


Factor 8x%5E2-32x to get 4%2A2x%28x-4%29.


Factor 21x%2B14 to get 7%283x%2B2%29.


%287%2A4%2A2x%283x%2B2%29%28x-3%29%28x-4%29%29%2F%284%2A7%28x-3%29%28x-4%29%283x%2B2%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


2x Simplify.



So %28%2821x%5E2-49x-42%29%2F%284x%5E2-28x%2B48%29%29%2F%28%2821x%2B14%29%2F%288x%5E2-32x%29%29 simplifies to 2x.


In other words,