Finding the restrictions on the variable of a problem

Question

4x²-2x          2x

-------     ÷ ------

x²+5x+4      x²+2x+1

Answer 1

First, multiply the first rational expression by the reciprocal of the second rational expression.

 

   (4x² - 2x)  *   (x² + 2x + 1)

__________________________    =

 

   (x² + 5x + 4) *  2x

 

 

Factor by taking out the GCF and using FOIL method.

 

 

  2x(2x - 1)  *  (x + 1) (x + 1)

_________________________     =

 

      (x + 4)(x + 1)  *  2x

 

 

 

Set the denominators equal to zero.

 

x + 4 = 0             x + 1 = 0            2x = 0

x = -4                  x = -1                   x = 0

 

The restrictions are

 

x = -4

x = -1

x = 0