Question

Divide (5x+20)/(x^(2)-5x-14)-:(x^(2)+7x+12)/(x+2) (Remember to flip the second fraction! )

Answer 1

The expression (5x+20)/(x^2 - 5x - 14) ÷ (x^2 + 7x + 12)/(x + 2) simplifies to 5/[(x-2)(x+3)] by flipping the second fraction and then doing multiplication and factoring.

Step-by-step explanation:

The process of dividing two fractions involves flipping (also known as finding the reciprocal of) the second fraction and then multiplying. The given expression is (5x+20)/(x^2 - 5x - 14) ÷ (x^2 + 7x + 12)/(x + 2). To do this, we can follow these steps:

1. Flip the second fraction to get (x + 2)/(x^2 + 7x + 12).
2. Multiply the two fractions to get [(5x+20)/(x^2 - 5x - 14)]*(x + 2)/(x^2 + 7x + 12).
3. Factor everything. The multiplication turns into [(5(x+4))/((x-2)(x+7))]*[(x + 2)/((x+4)(x+3))].
4. Cancel out the common factors to finish the simplification. You are left with 5/(x-2)*(1/x+3), which can be simplified further to 5/[(x-2)(x+3)].

Learn more about Fraction Division