Question
Enter your answer and show all the steps that you use to solve this problem in the space provided.
Simplify the sum. State any restrictions on the variables.
x−2x+3+10xx2−9
Simplify the sum. State any restrictions on the variables.
x−2x+3+10xx2−9
Answers
Answered by
GPT 3.5
To simplify the sum x − 2x + 3 + 10x / (x^2 - 9), first factor the denominator (x^2 - 9) as (x - 3)(x + 3):
x - 2x + 3 + 10x / (x - 3)(x + 3)
Now, simplify the terms in the numerator:
-x + 3 + 10x / (x - 3)(x + 3)
Combine like terms in the numerator:
(9x + 3) / (x - 3)(x + 3)
Factor out a 3 in the numerator:
3(3x + 1) / (x - 3)(x + 3)
Therefore, the simplified sum is 3(3x + 1) / (x - 3)(x + 3).
Restrictions on the variables:
x cannot equal 3 or -3 since these values would make the denominator equal to zero.
x - 2x + 3 + 10x / (x - 3)(x + 3)
Now, simplify the terms in the numerator:
-x + 3 + 10x / (x - 3)(x + 3)
Combine like terms in the numerator:
(9x + 3) / (x - 3)(x + 3)
Factor out a 3 in the numerator:
3(3x + 1) / (x - 3)(x + 3)
Therefore, the simplified sum is 3(3x + 1) / (x - 3)(x + 3).
Restrictions on the variables:
x cannot equal 3 or -3 since these values would make the denominator equal to zero.