Question

What values of X make this rational expression undefined?

Answer 1

This rational expression is undefined when the denominator equals 0, as it would return an undefined answer due to the inability to divide by 0.

Set the denominator to equal 0:

$x^2 + 2x - 24 = 0$

Since this is a trinomial, we need to find the factors that multiply into this expression. The factors will represent the zeros that we can plug into the equation to get it to equal 0.

The trinomial uses the following formula:

$ax^2 + bx + c$

Our b value is 2, and our c value is -24.

To find the factors, we need to find two numbers that multiply to -24, and two numbers that add up to 2.

Factors of 24: {1,2,3,4,6,8,12,24}

List out the sets of two factors that will multiply into 24:

{1,24}

{2,12}

{3,8}

{4,6}

Since b is 2, we will choose the set of two factors that have a difference of 2 between them. This means that we will use {4,6}, as there is a difference of 2 between these two numbers.

c is a negative value, and b is a positive value, so the bigger number will be the negative factor in this expression.

We now have our x-values: 4 and -6. These two values will make the expression equal 0.

To check that this is correct, plug these values into the equation:

$(4)^2 + 2(4) - 24 = 16 + 8 - 24 = 0$

$(-6)^2 + 2(-6) - 24 = 36 - 12 - 24 = 0$

x-values of -6 and 4 will make this rational expression undefined.