SOLUTION: simplify each rational expressions. state any restrictions on the variable x to the 2nd power minus nine divided by 2x+6

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Question 693780: simplify each rational expressions. state any restrictions on the variable
x to the 2nd power minus nine divided by 2x+6
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
To simplify %28x%5E2-9%29%2F%282x%2B6%29, you start by factoring numerator and denominator.
In the denominator, you can take out 2 as a common factor:
2x%2B6=2%28x%2B3%29
The numerator is a difference of squares, which is one of those special products you must have been taught about, maybe as
%28a%2Bb%29%28a-b%29=a%5E2-b%5E2.
So x%5E2-9=%28x%2B3%29%28x-3%29.

If x=3, the denominator is zero, and %28x%5E2-9%29%2F%282x%2B6%29 does not exist, it is undefined. x not = 0 is your restriction on the variable.

For any other value of x,
.

NOTE: You can write %28x%5E2-9%29%2F%282x%2B6%29 as (x^2-9)/(2x+6).
The parentheses are implied by the long horizontal fraction line in %28x%5E2-9%29%2F%282x%2B6%29,
but you need to write them out in (x^2-9)/(2x+6),
because otherwise you have
x^2-9/2x+6 = x%5E2-9%2F2x%2B6.