SOLUTION: I have read my textbook, and I don't understand. List all numbers for which the rational expression is undefined. x^2-4 ------ x^2+12x+27 Simplify 27a^7b^6 --------

Question 269519: I have read my textbook, and I don't understand.
List all numbers for which the rational expression is undefined.
x^2-4
------
x^2+12x+27

Simplify
27a^7b^6
--------
9a^8b^5

Simplify
-2y+6
------
-8y
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
List all numbers for which the rational expression is undefined.
(i)
to be undefined means that there is a zero in the denominator and this is not good. To find out where our expression is undefined, we set the denominator = 0 and solve. We get
(ii)
factoring this we get
(iii)
set each parenthesis = 0 and solve for x. We get
x = -9 and x = -3.
This tells us that pour expression will be undefined at x = -9 and x = -3.
-----
Simplify
(iv)
first reduce the coefficients (front numbers) to get
(v)
second, use rules of exponents: when you divide the same base, you subtract the exponents to get
(vi)
Now, if you want all exponents to be positive, then we get
(vii)
-----
Simplify
(viii)
The first step to simplify expressions is to look for a GCF. Here in the numerator it is 2. WE get
(ix)
reduce the -2 and -8 as
(x)
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