Final answer:
The simplified expression is obtained by factoring the polynomials and canceling out common terms in both the numerator and the denominator, resulting in 5/(x+3).
Step-by-step explanation:
To simplify the given expression, which is (x2-7x+10)/(x2-4)×(5x+10)/(x2-2x-15), we start by factoring each of the polynomials where possible. Specifically, we notice that x2-7x+10 can be factored into (x-5)(x-2), x2-4 into (x+2)(x-2), 5x+10 into 5(x+2), and x2-2x-15 into (x-5)(x+3). Now we write the expression with these factors:
((x-5)(x-2))/(x+2)(x-2))*(5(x+2))/(x-5)(x+3).
Next, we can eliminate terms that appear both in the numerator and the denominator. The (x-2) terms cancel out, as do the (x+2) terms and the (x-5) terms. We are left with:
5/(x+3).
Thus, the simplified expression is 5/(x+3), and we can check the answer by substituting different values for x to ensure it provides reasonable results that match the original expression before simplification.