anonymous
  • anonymous
1.what is the simplified form of x^4-81/x+3 2. what is the simplified form of x^2-25/X^2-3x-10 3. what is the excluded value of the rational expression 2x+6/4x-8
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
1. x^5+3x-81/x
radar
  • radar
This is actually three different and unrelated questions. Let's concentrate on No. 1. The key in simplifying this is to recognize a characteristic of the denominator. x^4-81. In time you should recognize that it is the difference of two perfect squares. Furthermore, in time or maybe right now you are familiar with factoring the difference of two squares \[a ^{2}-b ^{2}=(a+b)(a-b)\] does that strike a familiar chord?
anonymous
  • anonymous
yah

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radar
  • radar
O.K then we will factor \[x ^{4}-81=(x ^{2}+9)(x ^{2}-9)\] Look at both of those factors and what do you notice again?
anonymous
  • anonymous
yes i understand that one im lost on the second two
radar
  • radar
Specifically, what can you say about x^2-9 ???
radar
  • radar
O.K Lets focus on No. 2.
radar
  • radar
Again, what is the numerator? It is the difference of two perfect __________?
anonymous
  • anonymous
sqaures
radar
  • radar
\[x ^{2}-25\]right, and it is factored just like No. 1 what do you get?
anonymous
  • anonymous
im confused
radar
  • radar
(x+5)( _-_) ????
radar
  • radar
Did you work No. 1?
anonymous
  • anonymous
x-5
radar
  • radar
Yes (x+5)(x-5) that is the numerator. Now lets factor the denominator. It is a little more difficult.\[x ^{2}-3x-10\] When this is factored we are going to get something like this (x-a)(x+b) where -ab=-10 and -a+b=-3 The easiest way to do that is to look at the factors of 10 a b -1 +10 9 -2 +5 +3 -5 +2 -3 -10 +1 -9 Do you see a set that will work, a product of -10 and a sum of -3 ?
radar
  • radar
If you examine only one pair result in -3 so the factor is (x-5)(x+2)
radar
  • radar
Now write the complete problem: (x+5)(x-5) x+5 ----------- = ------ (x-5)(x+2) x+2 the x-5 cancel each other.
radar
  • radar
Suggest you repost No. 3. Good luck with these.

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