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

You are watching: What makes a rational expression undefined

x+3/x^2+x-20

Answer:


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Hi Chad,

A reasonable expression will always be undefined 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 also so we view the zeroes space x=4 and also x=-5.


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It looks prefer we are dealing with 1 the 2 expressions.

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

In either instance the technique is the same.

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

So set your denominator equal to zero and solve. This will determine the worths of x whereby the rational expression is undefined.

Based on exactly how the appropriate side that this expression is written, it looks like we"ll require some factoring.


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