siplify and state any restrictions on the variables.

x-2/x+3 plus 10x/x^2-9

Hope someone can explain this to me.

To simplify the expression (x-2)/(x+3) + (10x)/(x^2-9), we need to find a common denominator for both fractions. Let's break it down step by step:

First, let's look at the denominator of the first fraction, (x+3), and the denominator of the second fraction, (x^2-9).
The denominator x^2-9 can be factored as (x+3)(x-3). Since (x+3) is already a factor in the first fraction's denominator, the common denominator will be (x+3)(x-3).

Next, let's rewrite the fractions using the common denominator:
(x-2)/(x+3) = [(x-2)*(x-3)] / [(x+3)*(x-3)]
(10x)/(x^2-9) = [(10x)] / [(x+3)*(x-3)]

Now, we can combine the fractions together:
[(x-2)*(x-3)] / [(x+3)*(x-3)] + [(10x)] / [(x+3)*(x-3)]

To add the fractions, we need to have the same denominator for both fractions. Since they already have the same denominator of (x+3)(x-3), we can combine them directly:
[(x-2)*(x-3) + (10x)] / [(x+3)*(x-3)]

Now, let's simplify the numerator:
[(x-2)*(x-3) + (10x)]

Expanding the first term:
[(x^2 - 5x + 6) + (10x)]

Combining like terms:
x^2 - 5x + 6 + 10x

Simplifying further:
x^2 + 5x + 6 + 10x

Combining like terms again:
x^2 + 15x + 6

So, the simplified expression is (x^2 + 15x + 6) / [(x+3)*(x-3)].

Now, regarding the restrictions on the variables:
We need to consider the denominators (x+3) and (x-3). In order for the expression to be defined, these denominators cannot be equal to zero, as division by zero is undefined.

Hence, we have two restrictions:
1) x+3 ≠ 0, which means x ≠ -3.
2) x-3 ≠ 0, which means x ≠ 3.

Therefore, the expression is defined for all values of x except x = -3 and x = 3.