To solve the expression (x^2 + 2x - 8)/(x^2 + 3x - 10) * (x + 5)/(x^2 - 16), we can begin by factoring the quadratic expressions in the numerator and denominator of the first fraction:
(x^2 + 2x - 8)/(x^2 + 3x - 10) = ((x + 4)(x - 2))/((x + 5)(x - 2))
Similarly, we can factor the quadratic expression in the denominator of the second fraction:
(x + 5)/(x^2 - 16) = (x + 5)/((x + 4)(x - 4))
Substituting these expressions back into the original expression, we get:
((x + 4)(x - 2))/((x + 5)(x - 2)) * (x + 5)/((x + 4)(x - 4))
We can then cancel out the x - 2 and x + 4 factors in the numerator and denominator:
(x + 5)/(x - 4)
Therefore, the simplified expression is (x + 5)/(x - 4).