Find all numbers for which the rational expression is undefined. If the rational expression is defined for all real​ numbers, so state.

Question

Find all numbers for which the rational expression is undefined. If the rational expression is defined for all real​ numbers, so state.

x+3/x^2+x-20

Answer:

Answer 1

Hi Chad,

A rational expression will always be undefined at precisely the values of x that make the denominator zero since division by zero is undefined. So, in this case, we need to determine the zeroes of the denominator x² + x - 20.

Factoring this polynomial we have x² + x - 20 = (x+5)(x-4) and so we see the zeroes are x=4 and x=-5.

Answer 2

It looks like we are dealing with 1 of 2 expressions.

1. x+ 3/x^2+x-20
2. x+3/(x^2+x-20)

In either case the method is the same.

In the case of division, we must find any values of x that evaluate the denominator equal to zero.

So set your denominator equal to zero and solve. This will identify the values of x where the rational expression is undefined.

Based on how the right side of this expression is written, it looks like we'll need some factoring.