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.
|
|
|
