help simpllify and solve

Question

 

x^2 - 7x + 12/x+ 4 divide with x^2 - 7x + 12/x^2 + 6x + 8

 

 

Thank you

Answer 1

Hi L

I believe the equation is written as this....

 

(x² - 7x + 12) ÷ (x² - 7x + 12)

    (x + 4)           (x² + 6x + 8)

 

First, we'll break them down into their factors;

 

(x² - 4x - 3x + 12) ÷ (x² - 4x -3x + 12)

      (x + 4)               (x² + 4x + 2x + 8)

 

Still getting their factors

 

(x² - 4x) - (3x + 12) ÷ (x² - 4x) - (3x +12)

         (x + 4)               (x² + 4x) + (2x + 8)

 

Still getting their factors

 

x(x - 4) - 3(x - 4) ÷   x(x - 4) -3(x -4)

        (x + 4)           x(x + 4) + 2(x + 4)

 

Still getting their factors

 

(x - 3)(x - 4) ÷ (x - 3)(x - 4)

    (x + 4)        (x + 2)(x + 4)

 

 

Now just like dividing fractions where we have a/b ÷ c/d which become a/b * d/c; we'd apply that principle here;

 

(x - 3)(x - 4) × (x + 2)(x + 4)

    (x + 4)         (x - 3)(x - 4)

 

That would give us;

 

(x - 3)(x - 4)(x + 2)(x + 4)

    (x + 4)(x - 3)(x - 4)

 

Now in this step, like terms cancel out;

that would be (x - 3) cancelled out by (x - 3); (x - 4) by (x - 4) and (x + 4) by (x + 4) leaving us with

(x + 2) at the top and 1 at the bottom

 

(x + 2)

    1

 

which is simple (x + 2).........................................Your Final Answer.

Answer 2

 X ^2 - 7x +12   ÷   X^2 -7X + 12 =

   X  +4                   X^2 + 6X + 8 

 

 

  X^2 - 7x + 12 *   X^2 +6x + 8  =

     X + 4               X^2 - 7X + 12

 

   ( X^2 - 7x + 12) is crossed out, and X^2 + 6x + 8 will be factored to ( X+4 ) ( X +2)

 

     ( X + 4 ) ( X+2)

         X  + 4

      

      X + 2