write the rational expression in simplest terms be sure to identify what values of the variale will make the denominator undefined

Question

(x(x+1)^2(x-5))/(x(x+2)(x-5)^3)

Answer 1

x(x+1)²(x-5)

-----------------

x(x+2)(x-5)³

 

This will be undefined for any value of x that

makes the denominator equal to zero...

Undefined at x=0, x=-2, x=5

 

For simplifying we can cancel the factors that

are the same in the numerator and denominator

 

x(x+1)²(x-5)             (x+1)²
-----------------  =   --------------
x(x+2)(x-5)³              (x+2)(x-5)²

Answer 2

Your expression is already in simplest form, since each factor of the expression is linear.  Now just set the denominator equal to zero to find undefined values.

 

x(x+2)(x-5)(x-5)(x-5)=0