SOLUTION: <pre> Simplify the expression: x² - 9 4x² - 12x + 36 ———————————— × ———————————————— 2x² - 8x + 6 x³ + 27</pre>

Algebra.Com
Question 38537This question is from textbook
: 
    Simplify the expression: 

   x² - 9       4x² - 12x + 36 
———————————— × ————————————————
2x² - 8x + 6        x³ + 27
 This question is from textbook

Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!


   x² - 9       4x² - 12x + 36 
———————————— × ————————————————
2x² - 8x + 6        x³ + 27

Factor each numerator and denominator:

Left numerator:     x² - 9 = x² - 3² = (x - 3)(x + 3)

Left denominator:   2x² - 8x + 6 = 2(x² - 4x + 3) = 2(x - 3)(x - 1)

Right numerator:    4x² - 12x + 36 = 4(x² - 3x + 9)

Right denominator:  x³ + 27 = x³ + 3³ = (x + 3)(x² - 3x + 9)

  (x - 3)(x + 3)        4(x² - 3x + 9)
————————————————— × ——————————————————————                
 2(x - 3)(x - 1)     (x + 3)(x² - 3x + 9)

Indicate multiplication of numerators and denominators:

     4(x - 3)(x + 3)(x² - 3x + 9)
—————————————————————————————————————                
 2(x - 3)(x - 1)(x + 3)(x² - 3x + 9)

Cancel 2 and 4

     2
     4(x - 3)(x + 3)(x² - 3x + 9)
—————————————————————————————————————                
 2(x - 3)(x - 1)(x + 3)(x² - 3x + 9)
 1

Cancel the (x - 3)'s

     2   1 
     4(x - 3)(x + 3)(x² - 3x + 9)
—————————————————————————————————————                
 2(x - 3)(x - 1)(x + 3)(x² - 3x + 9)
 1   1

Cancel the (x + 3)'s

     2   1      1
     4(x - 3)(x + 3)(x² - 3x + 9)
—————————————————————————————————————                
 2(x - 3)(x - 1)(x + 3)(x² - 3x + 9)
 1   1             1

Cancel the (x² - 3x + 9)'s

     2   1      1          1
     4(x - 3)(x + 3)(x² - 3x + 9)
—————————————————————————————————————                
 2(x - 3)(x - 1)(x + 3)(x² - 3x + 9)
 1   1             1         1

                 2
              ———————
               x - 1 

Edwin
AnlytcPhil@aol.com
RELATED QUESTIONS

solve for x 
                    ________________________
          (answered by Alan3354)


Multiply 

  2x² - x - 3      3x² - 11x - 20
——————————————— × ————————————————
  (answered by AnlytcPhil)

if ABCD is similar to EFGD then x=


                  \  A___________5___________B
 (answered by Cromlix)


Simplify the expression. Assume that all variables 
represent nonzero integers. 

 (answered by AnlytcPhil)

solve for x

                   
... (answered by Edwin McCravy)


I need help with some Pre-Algebra Eqautions

1. 3x - 5 - 2x = 8 - 9


2. 8x + 7  (answered by ichudov,AnlytcPhil)

Simplify:


        
        ((x^(3/2))y^-3)^1/3
        --------------------
    (answered by jim_thompson5910)


Find the missing number
27   74   215
12   x     80
39  110... (answered by Edwin McCravy,ikleyn)