Find any numbers for which the rational expression is undefined. Harder Version.

Question

Find any numbers for which the rational expression is undefined.

 

2x^5+7 / 2x^2+10x

 

or:

 

2x⁵+7

________

2x²+10x

 

Ok, so I understand to set the denominator to zero. In this case I need to factor first and am expecting to have two equations in brackets to set to zero. The problem I'm having is that I can only seem to factor this to 2x(x+5) which is easy to do in my head. I also tried to use the AC method to see if I would come up with a different result and I did not, also I took note that this is not the difference of two squares either. I do not understand how to go from here :( I appreciate any help thanx!

 

 

Answer 1

Your approach of setting  2x² + 10x equal to zero and factoring it was correct.  Also, you are right that this is not a difference of perfect squares, being that there is no minus sign anywhere or numbers that are perfect squares. You cannot simplify nor factor this rational expression any further.

 

This is what we need to do next.  Set the factors of 2x² + 10x equal to zero.

 

2x = 0         and       x + 5 = 0

 

x = 0           and       x = -5

 

 

You will have two values of x that will make the rational expression undefined.

 

x = -5        and      x = 0