Find all numbers for which the rational expression is not defined.

Question

Find all numbers for which the rational expression is not defined.

 

1.X+8/x^2-64

 

2.x^2-4x-32/x^2-4x-12

Answer 1

   x+8               (x+8)

-----------  =  --------------

(x²-64)         (x+8)(x-8)

 

We can't have the denominator = 0, which happens when x = 8 or x= -8.  Hence the expression is not defined at these values.  The expression simplifies to 1/(x-8), but it is still undefined at both x = 8 and x = -8.

 

x²-4x-32          (x-8)(x+4)

-------------  =  ---------------

x²-4x-12          (x-6)(x+4)

 

Again, the denominator equals zero when x = 6 or -4,, so the expression is not defined at these values of x.  The expression simplifies to (x-8)/(x-6), but it is still undefined at both x = 6 and x = -4.