SOLUTION: This problem is on my study guide for my final tomorrow (06/28/11)! Please help! I'm not sure if this even falls under just "Equations." x²-16 over x²+6x+8 and x²-3x-10 over x

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Question 464931: This problem is on my study guide for my final tomorrow (06/28/11)! Please help! I'm not sure if this even falls under just "Equations."
x²-16 over x²+6x+8
and x²-3x-10 over x²-25


Found 2 solutions by josmiceli, ewatrrr:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!

Anything that looks like this, usually you
must factor the top, bottom, or both.
Here you must factor both top and bottom
--------------------------------
The top is the difference of 2 squares, and the factors
always look like because the
middle term gets subtracted out like this:

---------------------------------
A good way to factor the bottom is to " complete
the square"
First set the expression equal to zero,
Then subtract from both sides
Take 1/2 the coefficient of , square it, and
add it to both sides



Take the square root of both sides


and


The factors are and
Now the original fraction looks like:

This is the same as:

-------------------------------------
The 2nd problem has the difference of 2 squares on the bottom
You can factor the top just as in the 1st problem.
The bottom is:
When you complete the squares, the top is:

Now you have:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 

Hi,

factoring numerator and denominator:

x^2 - 16 = (x-4)(x+4)

x^2 + 6x + 8 = (x+2)(x+4)





x^2 - 3x + 10 = (x-5)(x+2)

x^2 - 25 = (x-5)(x+5)



 

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