SOLUTION: How do I simplify this rational expression? (3x^2 + 9) / (x^2 -9)

Question 635934: How do I simplify this rational expression?
(3x^2 + 9) / (x^2 -9)

Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
When simplifying algebraic expressions, remember to factor, factor, factor! Then look for common (like) factors in the numerator and denominator so that you can "cancel" them. Actually their ratio is equal to one - the multiplicative identity, which we know does not change the product.
Restricting our solution domain to real numbers only, the numerator of the given expression factors into 3(x^2+3). The denominator is of the form, "the difference of two perfect squares", (x^2 - 3^2), which factors into (x+3)(x-3). The rational expression becomes [3(x^2+3)]/[(x+3)(x-3)]. As you can see, none of the factors are the same, thus no further simplification is possible, and this is your final answer.
If we allow for complex numbers that include an imaginary term the factor (x^2+3) can be factored into [x+i*sqrt(3)][x-i*sqrt(3)], where i=sqrt(-1). In either case none of the factors are the same and the answer is as given above.
RELATED QUESTIONS
How do I simplify this expression:... (answered by mathbird)

How do I simplify this expression completely? 45(x/5 +... (answered by Cromlix)

I need help multiplying this rational expression. x+9/x-3 *... (answered by jim_thompson5910)

X^2 + 3x +2/ -3x -x^2 -2 i need to simplify this rational expression (answered by Fombitz)

x4-5x2+4 ________ How do I Simplify this rational expression... (answered by josgarithmetic)

how do I simplify... (answered by lynnlo,Alan3354)

I am currently taking Intermediate Algebra, I am having problems with rational... (answered by stanbon)

Simplify the rational expression. {{{(3/x+4)/((9)/(x^2)-16)}}} Please help me... (answered by htmentor)

How do I solve this equation? Do the operations & Simplify... (answered by 303795)