Find all numbers because that which the rational expression is undefined. If the rational expression is defined for all real​ numbers, for this reason state.

You are watching: When is a rational expression undefined

x+3/x^2+x-20

Answer:


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Hi Chad,

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

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


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It looks prefer we are handling 1 of 2 expressions.

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

In either instance the method is the same.

In the situation of division, we should find any kind of values of x that evaluate the denominator equal to zero.

So set your denominator same to zero and also solve. This will determine the worths of x where the reasonable expression is undefined.

Based on just how the best side of this expression is written, that looks favor we"ll require some factoring.


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