I=x^2−16/√x^2+3x −2 con x∈A⊆R .

Step 1: Consider the given function

I = \frac{x^2 - 16}{\sqrt{x^2 + 3x - 2}}

Step 2: Factorize the numerator and simplify the denominator.

x^2 - 16 = (x - 4)(x + 4)

x^2 + 3x - 2 can be factored into:

\sqrt{(x + 4)(x - 1)}

Step 3: Put the factored expressions back into the original fraction:

I = \frac{(x - 4)(x + 4)}{\sqrt{(x + 4)(x - 1)}}

Step 4: Simplify the expression:

I = \sqrt{\frac{(x - 4)(x + 4)^2}{(x - 1)(x + 4)}}

I = \frac{(x + 4)(x - 4)}{\sqrt{(x + 4)(x - 1)}}

As a result, the simplified solution is:

I = \frac{x^2 - 16}{\sqrt{x^2 + 3x - 2}}

Therefore, the final answer is:

I = \frac{x^2 - 16}{\sqrt{x^2 + 3x - 2}}