SOLUTION: Show each step in multiplying/dividing the following rational expressions: a. [(2x^2 - x - 3))/(3x^2 + 7x + 4)] · [(3x^2 - 11x - 20)/(4x^2 - 9)]

Algebra ->  Expressions-with-variables -> SOLUTION: Show each step in multiplying/dividing the following rational expressions: a. [(2x^2 - x - 3))/(3x^2 + 7x + 4)] · [(3x^2 - 11x - 20)/(4x^2 - 9)]       Log On


   

Question 22393: Show each step in multiplying/dividing the following rational expressions:
a. [(2x^2 - x - 3))/(3x^2 + 7x + 4)] · [(3x^2 - 11x - 20)/(4x^2 - 9)]

Answer by AnlytcPhil(1807) About Me  (Show Source):
You can put this solution on YOUR website!
Show each step in multiplying/dividing the 
following rational expressions: 
a. 

  2x2 - x - 3     3x2 - 11x - 20
—————————————— · ————————————————
 3x2 + 7x + 4        4x2 - 9

Factor all numerators and denominators:

 (2x-3)(x+1)     (3x+4)(x-5)
————————————— · ——————————————
 (3x+4)(x+1)     (2x-3)(2x+3)

Put all the numerator and denominator factors 
together as one fraction.

 (2x-3)(x+1)(3x+4)(x-5)
—————————————————————————
 (3x+4)(x+1)(2x-3)(2x+3)
 
Cancel the (2x-3)'s
  
    1
 (2x-3)(x+1)(3x+4)(x-5)
—————————————————————————
 (3x+4)(x+1)(2x-3)(2x+3)
              1

 (x+1)(3x+4)(x-5)
———————————————————
   (3x+4)(x+1)


Cancel the (x+1)'s

   1
 (x+1)(3x+4)(x-5)
———————————————————
   (3x+4)(x+1)
           1

 (3x+4)(x-5)
—————————————
   (3x+4)

Cancel the (3x+4)'s

   1 
 (3x+4)(x-5)
—————————————
   (3x+4)
     1

  (x-5)
 ———————
    1 

or just

   x-5

Edwin
AnlytcPhil@aol.com