Question

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

Answer 1

1. x^5+3x-81/x

Answer 2

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?

Answer 3

yah

Answer 4

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?

Answer 5

yes i understand that one im lost on the second two

Answer 6

Specifically, what can you say about x^2-9 ???

Answer 7

O.K Lets focus on No. 2.

Answer 8

Again, what is the numerator? It is the difference of two perfect __________?

Answer 9

sqaures

Answer 10

\[x ^{2}-25\]right, and it is factored just like No. 1 what do you get?

Answer 11

im confused

Answer 12

(x+5)( _-_) ????

Answer 13

Did you work No. 1?

Answer 14

x-5

Answer 15

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 ?

Answer 16

If you examine only one pair result in -3 so the factor is (x-5)(x+2)

Answer 17

Now write the complete problem:

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

the x-5 cancel each other.

Answer 18

Suggest you repost No. 3. Good luck with these.