Final answer:
The correct next step for adding the fractions with different denominators is to rewrite them with a common denominator, which is achieved in option c: x/(x+5)(x-3) + (4(x-3))/(x+5)(x-3).
Step-by-step explanation:
The correct next step for Tamika to find the least common denominator (LCD) and to add the two fractions x/(x²+2x-15) and 4/(x+5) is to first factor the denominator of the first fraction. The factored form of x²+2x-15 is (x+5)(x-3), which is the least common denominator she found. Therefore, option c is the correct next step: she should rewrite the fractions with the common denominator, resulting in x/(x+5)(x-3) + (4(x-3))/(x+5)(x-3). She does this by multiplying the numerator and denominator of the second fraction by (x-3), which is the term from the LCD that is missing in its denominator.