Question Video: Determining the Common Domain of Two Rational Fractions

Determine the common domain of the functions 𝑛₁(π‘₯) = (βˆ’7)/(π‘₯ βˆ’ 7) and 𝑛₂(π‘₯) = (βˆ’8)/(π‘₯Β² βˆ’ 64).

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Video Transcript

Determine the common domain of the functions 𝑛 one of π‘₯ equals negative seven divided by π‘₯ minus seven and 𝑛 two of π‘₯ equals negative eight divided by π‘₯ squared minus 64.

To find a common domain, we need to set the denominators equal to zero, solve for π‘₯, and then exclude those values. So the reason why we set the denominators equal to zero is because the denominators are on the bottom, and you never want to divide by zero because that would give you an answer that is undefined. So we set our denominators equal to zero, solve for π‘₯, and we will exclude these values.

So let’s add seven to the left equation and then add 64 to the right equation. So we already know we’re gonna have to exclude seven. And on the right equation, let’s square root both sides. So we get π‘₯ equals eight and π‘₯ equals negative eight because the square root of 64 is positive eight and negative eight.

So the common domain between these functions would be all real numbers minus negative eight, seven, and eight.

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