Question

Tamika found that the least common denominator needed to add x/x²+2x-15 + 4/x+5 is (x+5)(x-3). Which is a correct next step?

a. (x+4)/(x+5)(x-3)
b. x/(x+5)(x-3) + (4(x+5))/(x+5)(x-3)
c. x/(x+5)(x-3) + (4(x-3))/(x+5)(x-3)
d. (x(x+5)(x-3))/(x+5)(x-3) + (4(x+5)(x-3))/(x+5)(x-3)

Answer 1

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.