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 --------

Algebra ->  Polynomials-and-rational-expressions -> 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 --------       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
List all numbers for which the rational expression is undefined.
(i) %28x%5E2-4%29+%2F+%28x%5E2%2B12x%2B27%29
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) %28x%5E2%2B12x%2B27%29+=+0+
factoring this we get
(iii) %28x%2B9%29%28x%2B3%29+=+0
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) 27a%5E7b%5E6+%2F+9a%5E8b%5E5
first reduce the coefficients (front numbers) to get
(v) 3a%5E7b%5E6+%2F+a%5E8b%5E5
second, use rules of exponents: when you divide the same base, you subtract the exponents to get
(vi) 3a%5E%28-1%29b%5E1
Now, if you want all exponents to be positive, then we get
(vii) 3b%2Fa
-----
Simplify
(viii) %28-2y%2B6%29%2F-8y
The first step to simplify expressions is to look for a GCF. Here in the numerator it is 2. WE get
(ix) -2%28y+-+3%29%2F%28-8y%29
reduce the -2 and -8 as
(x) %28y-3%29%2F%284y%29