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Find all real numbers for which the rational expression is undefined. See Example.

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EXAMPLE uncover all genuine numbers for which the expression is undefined:

a.

\"*\"

b.

\"*\"

c.

\"*\"

d.

\"*\"

Strategy To find the real numbers for which every expression is undefined, we will find the values of the variable the make the denominator 0.

Why we don\"t should examine the molecule of the reasonable expression; it have the right to be any kind of value, including 0. It\"s a denominator that 0 that renders a rational expression undefined, because a denominator the 0 indicates division by 0.

Solution

a. The denominator the

\"*\"
will certainly be 0 if we change x with 5.

\"*\"

Since

\"*\"
is undefined, the expression
\"*\"
is undefined for x = 5.

b.

\"*\"
will be unknown for values of x the make the denominator 0. To find these values, we set x2 − x − 6 same to 0, and solve for x.

\"*\"

Since 3 and −2 make the denominator 0, the expression

\"*\"
is undefined because that x = 3 and x = −2. To inspect the results, we continue as follows.

\"*\"

c. No issue what genuine number is substituted for x, the denominator, x2 + 1, will not be equal to 0. (A number squared to add 1 cannot same 0.) Thus, no real numbers do

\"*\"
undefined.

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d. Since the denominator the

\"*\"
does not contain a variable, the denominator have the right to never be equal to 0. Thus, no genuine numbers make the expression undefined.