Question

Enter the correct answer in the box. Write the factored form of the least common denominator needed to simplify this expression. (g+1/g^2 + 2g - 15)+ (g+3/g+5)

Answer 1

To simplify the given expression, the least common denominator in its factored form is (g+5)(g-3). The LCD is identified by factoring the quadratic denominator of the given expressions.

Step-by-step explanation:

If we are to find the factored form of the least common denominator (LCD) to simplify the expression (g+1/g^2 + 2g - 15) + (g+3/g+5), we need to factor the denominators. The quadratic g^2 + 2g - 15 can be factored into (g+5)(g-3). Since g+5 is already presented in one of the fractions, the LCD will simply be the product of (g+5)(g-3) and (g+5), which is (g+5)(g-3). So, the factored form of the LCD is (g+5)(g-3).

To simplify expressions with different denominators, we find the LCD, rewrite each fraction with the LCD, and then add or subtract the numerators.

Answer 2

(g+5)x(g-3)

Step-by-step explanation:

Edmentum/PLATO answer:

Rewrite the expression:

g+1/g^2+5g-3g-15 + g+3/g+5

Factor out g from expression:

g+1/gx(g+5)-3g-15 + g+3/g+5

Factor out g+5:

g+1/(g+5)x(g-3) + g+3/g+5

Least common denominator: (g+5)x(g-3)