Question

Already tried simplifying and dividing, but i didn't get the correct answer. Could a step by step explanation be provided so i know how to do this in the future?

Answer 1

Answer:

$\sf \dfrac{x+2}{x}$

Step-by-step explanation:

Simplifying the expression:

 1. Factorize each expression.

     x² + 8x + 15

   Sum = 8

  Product = 15

  Factors = 3 , 5  {When we add 3 & 5 we get 8 and when we multiply 3*5, we get 15}

  x² + 8x + 15 = x² + 3x + 5x + 15

                     = x(x + 3) + 5(x + 3)

                     = (x + 3)(x + 5)

x² - 2x - 15

 Sum = -2

Product = -15

Factors = 3 , (-5)  {When we add 3 + (-5) =2 and when we multiply, 3*(-5) = -15}

x² - 2x - 15 = x²  + 3x - 5x - 15

                 =x(x + 3) -5(x + 3)

                 = (x + 3)(x - 5)

x² + 5x = x( x + 5)

x² - 3x - 10

Sum = -3

Product = -10

Factors = 2 , (-5)  {When we add 2 +(-5) = -3 and when we multiply 2 *(-5) = -10}

x² - 3x - 10 = x² + 2x - 5x - 10

                 =x(x + 2) - 5(x + 2)

                 = (x + 2)(x - 5)

2. Use KCF method and simplify.

  K - keep the first fraction

  C - change division to multiplication

 F -  Flip the second fraction.

$\sf \dfrac{x^2 + 8x + 15}{x^2 - 2x - 15} \ \div \ \dfrac{x^2 + 5x}{x^2 - 3x - 10}=\dfrac{x^2 + 8x + 15}{x^2-2x - 12}*\dfrac{x^2 - 3x - 10}{x^2 + 5x}$

                                              $\sf = \dfrac{(x +3)*(x +5)}{(x+3)(x - 5)}*\dfrac{(x + 2)(x - 5)}{x(x+5)} \\\\= \dfrac{x + 2}{x}$