SOLUTION: Simplify each rational expression. State any restrictions on the variable. 1. 3x^2-12/x^2-x-6 I got 3(x-2)/(x-3) x cannot be equal to 3 and -2. I'm not sure if my restrictions a

Question 196760: Simplify each rational expression. State any restrictions on the variable.
1. 3x^2-12/x^2-x-6
I got 3(x-2)/(x-3) x cannot be equal to 3 and -2.
I'm not sure if my restrictions are correct. Could someone please check them?
Simplify each sum or difference.
4(x+3)/(x-1)(x+2) + (x-2)(x+3)/(x-1)
I got 4(x+3)+(x-2)(x+3)/(x-1) which is equivalent to 4(x+3)+x^2+x-6/(x-1)
I'm not sure if I did this correctly...
Could someone check?
Thank you!
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
1st problem
.
Exactly correct , congrats
now @x=-2, we have a "hole" due to cancelling (x+2)
and at x=3, we have an asymptote ,,,,due to (x-3) in denominator
zero at x=2, due to (x-2) in num
.
2 nd problem
.
4 (x+3) / { (x-1) (x+2) } + { (x+3) (x-2) } / (x-1)
.
Use LCD of (x-1) (x+2)
.
[ 4 (x+3) + { (x+3)(x-2)(x+2) } ] / [ (x-1) (x+2) ]
.
[ (x+3) { 4 + (x-2)(x+2) } ] / (x-1)(x+2)
.
[ (x+3) { 4 + x^2 -4} ] / (x-1)(x+2)
.
{ (x+3) x^2 }/ (x-1)(x+2)
.
(x^3 +3x^2 ) / (x-1)(x+2)
.
Asymptotes at x=1, x=-2,,,,,,due to (x-1)(x+2) in den
zero's at x=0,,x=-3,, due to factors in num
.
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