x-2/x+3 + 10x/x^2-9
I got x+2/x-3
But I need to know if there are any restrictions on the variables.
I think the answer is if the denominator is equal to zero.
Yes, you got the concept correct,
now, for what values of x does x-3 and x^2 - 9 equal to zero ?
To find the restrictions on the variables, we need to identify the values that would make the denominator of any fraction become zero. When the denominator is zero, the fraction is undefined.
For the given expression:
(x - 2)/(x + 3) + 10x/(x^2 - 9)
Let's examine the denominators. The first denominator is (x + 3), and the second denominator is (x^2 - 9).
When is (x + 3) equal to zero?
x + 3 = 0
x = -3
So, the value x = -3 would make the first denominator zero.
Now, let's consider the second denominator:
x^2 - 9 = 0
This is a quadratic equation that can be factored as (x - 3)(x + 3) = 0.
So, the two solutions are x = 3 and x = -3.
However, we already found that x = -3 makes the first denominator zero, meaning x = -3 is restricted.
Therefore, the restrictions on the variable x for this expression are x ≠ -3.
Hence, the simplified expression is (x + 2) / (x - 3) with the restriction that x ≠ -3.