what is x^2_3x+2/x^2-16+3x+6/x^2-16
To simplify the given expression, we need to perform the operations of addition and division step by step. Let's break it down:
The expression is:
(x^2 - 3x + 2) / (x^2 - 16) + (3x + 6) / (x^2 - 16)
Step 1: Factor the denominators
The first step is to factor the denominators (x^2 - 16) on both terms:
(x^2 - 3x + 2) / [(x - 4)(x + 4)] + (3x + 6) / [(x - 4)(x + 4)]
Step 2: Find a common denominator
To add the fractions, we need a common denominator. In this case, since both fractions have the same denominator, we already have a common denominator.
Step 3: Combine the numerators
Next, we can combine the numerators of both fractions:
(x^2 - 3x + 2 + 3x + 6) / (x - 4)(x + 4)
Simplifying the numerator:
(x^2 + 2 + 6) / (x - 4)(x + 4)
(x^2 + 8) / (x - 4)(x + 4)
So, the simplified expression is (x^2 + 8) / (x - 4)(x + 4).