Question 269519
List all numbers for which the rational expression is undefined.
(i) {{{(x^2-4) / (x^2+12x+27)}}}
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) {{{(x^2+12x+27) = 0 }}}
factoring this we get
(iii) {{{(x+9)(x+3) = 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.
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Simplify 
(iv) {{{27a^7b^6 / 9a^8b^5}}} 
first reduce the coefficients (front numbers) to get
(v) {{{3a^7b^6 / a^8b^5}}} 
second, use rules of exponents: when you divide the same base, you subtract the exponents to get
(vi) {{{3a^(-1)b^1}}} 
Now, if you want all exponents to be positive, then we get
(vii) {{{3b/a}}}
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 Simplify
(viii) {{{(-2y+6)/-8y}}}
The first step to simplify expressions is to look for a GCF. Here in the numerator it is 2. WE get
(ix) {{{-2(y - 3)/(-8y)}}}
reduce the -2 and -8 as
(x) {{{(y-3)/(4y)}}}