Add or subtract and simplify if possible:
2x + 9 -36
---- --- ---------
x+3 x-3 x^2-9
Don't try to "create" fractions in this format, the spacing comes out all wrong.
did you mean:
2x/(x+3) + 9/(x-3) - 36/(x^2 - 9) ??
if so, notice that x^2-9 = (x+3)(x-3) , so your LCD is
(x+3)(x-3)
give it a try
Thanks I did
To add or subtract algebraic fractions, we need a common denominator. In this case, the common denominator will be (x+3)(x-3)(x^2-9). Let's break down the steps to simplify the expression:
1. Factorize the expressions:
- (x+3)(x-3) can be factored as (x^2 - 9) using the difference of squares formula.
- (x^2 - 9) can be factored as (x+3)(x-3) using the same difference of squares formula.
2. Now, rewrite the expression with these factored denominators:
2x/(x+3)(x-3)(x^2-9) + 9/(x+3)(x-3)(x^2-9) - 36/(x+3)(x-3)(x^2-9)
3. Simplify the numerators:
We'll combine the numerators over the common denominator.
2x + 9 - 36 = 2x - 27
4. Keep the common denominator:
The common denominator remains unchanged as (x+3)(x-3)(x^2-9).
5. Put it all together:
The simplified expression is (2x - 27)/(x+3)(x-3)(x^2-9).
Note: Please make sure to check for any restrictions on the domain. In this case, we need to ensure that x ≠ -3, 3, because these values would make the denominator equal to zero, resulting in an undefined expression.