SOLUTION: n^2-9-20/2n^2 x n^2+5n/n^2-25

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Question 85478: n^2-9-20/2n^2 x n^2+5n/n^2-25
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given expression (note: it should be n%5E2+-+9%2An+%2B+20 not n%5E2+-+9%2An+-+20)


Factor the first numerator (note: if you need help with factoring, check out this solver)




%28%28%28n-4%29%28n-5%29%29%2F%282n%5E2%29%29%2A%28%28n%28n%2B5%29%29%2F%28n%5E2+-+25%29%29 Factor the second numerator


Factor the second denominator

Notice we have these common terms

They divide and cancel out

%28%28n-4%29%2F%282n%5E2%29%29%28n%2F1%29
Now divide n and 2n%5E2 to get 1%2F2n

%28n-4%29%2F%282n%29
So the expression



simplifies to

%28n-4%29%2F%282n%29



As always, we can verify our answer. We can graph the original expression



as a function of x and y like this

graph of

and graph the simplified result

%28n-4%29%2F%282n%29

+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C%28x-4%29%2F%282x%29%29 graph of y=%28x-4%29%2F%282x%29

Since they produce the same graphs, this means they are equivalent. Since they are equivalent, this means that our answer has been verified.