Question

Divide as indicated. Simplify the answer. (x²+10x+24)/(x²+4x-12)-:(x²+2x-8)/(3x-6)

Answer 1

To divide the given expression, simplify both fractions by factoring the quadratic expressions in the denominators. Then, use the division rule for fractions by multiplying the numerators and denominators. The final expression is (x²+10x+24)/(x+6)/(x+4).

Step-by-step explanation:

To divide the given expression, we need to first simplify both fractions by factoring the quadratic expressions in the denominators. Then, we can use the division rule for fractions which states that dividing by a fraction is the same as multiplying by its reciprocal. Here are the step-by-step instructions:

1. Factor the first denominator: (x²+4x-12) = (x+6)(x-2)
2. Factor the second denominator: (x²+2x-8) = (x+4)(x-2)
3. Reciprocal of the second fraction: 1/((x+4)(x-2))
4. Multiply the numerators: (x²+10x+24) * 1 = x²+10x+24
5. Multiply the denominators: (x+6)(x-2) * 1/((x+4)(x-2)) = (x+6)/(x+4)
6. Combine the simplified fractions: (x²+10x+24)/(x+6)/(x+4)