33.2k views
3 votes
Multiply: (x²+5x+6)/(x²-6x+9)*(5x-15)/(x²-9) and simplify your answer

User Bencallis
by
8.5k points

1 Answer

2 votes

Final answer:

The expression (x²+5x+6)/(x²-6x+9) * (5x-15)/(x²-9) simplifies to 5(x+2)/(x-3) after factoring out common terms in the numerator and denominator and then canceling them out.

Step-by-step explanation:

To multiply and simplify the expression (x²+5x+6)/(x²-6x+9) * (5x-15)/(x²-9), we first look for factors that can cancel out to simplify the expression.

The first step is to factor the quadratics where possible. The numerator x²+5x+6 can be factored into (x+2)(x+3). The denominator x²-6x+9 is a perfect square and can be factored into (x-3)(x-3) or (x-3)². The second numerator 5x-15 can be factored out to 5(x-3), and the second denominator x²-9 is a difference of squares, which factors into (x+3)(x-3).

Thus the expression becomes:

(x+2)(x+3) / (x-3)² * 5(x-3) / (x+3)(x-3)

We can cancel out the common terms (x+3) and (x-3) present in both the numerator and the denominator, leading to further simplification:

(x+2) / (x-3) * 5

Multiplying the remaining terms gives us the final simplified expression:

5(x+2)/(x-3)

This simplified result is our answer.

User Oodini
by
7.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories