Find the sum and express in simplest form. (x^2)/(x^2-9)+(2x-15)/(x^2-9)
combine the numberator terms:
x^2 + 2x -15
which is factorable
(x+5)(x-3)
Factor the denominator
(x+3)(x-3)
simplify.
To simplify the expression, we need to find the common denominator of the two fractions, which is (x+3)(x-3), the factored form of the denominator.
Now, we can rewrite the original expression as:
[(x^2 + 2x -15) / (x+3)(x-3)]
Next, we want to try to simplify the numerator. The numerator is already in factored form, so we don't need to do any further factorization.
So, the simplified expression becomes:
[(x+5)(x-3) / (x+3)(x-3)]
Now, we can cancel out the common factors (x-3) in the numerator and denominator to further simplify the expression:
[(x+5) / (x+3)]
Therefore, the simplified expression is: (x+5) / (x+3)