Find the domain of the rational function. Then, write it in lowest terms. f(x)=x2+9x−3f\left(x\right)=\frac{x^2+9}{x-3}f(x)=x−3x2+9

{x∣x≠3}, f ( x ) = x 2 + 9 x − 3 f\left(x\right)=\frac{x^2+9}{x-3} f ( x ) = x − 3 x 2 + 9

Find the domain of the rational function. Then, write it in lowest terms. f ( x ) = x 2 + 9 x − 3 f\left(x\right)=\frac{x^2+9}{x-3} f ( x ) = x − 3 x 2 + 9

Hey, everyone. Let's take a look at this practice problem. Here, we want to find the domain of the rational function and then write it in lowest terms. So let's go ahead and start by finding the domain. Now when we find the domain, we want to take our denominator and set it equal to 0. So here doing that, I can go ahead and solve for x by simply adding 3 to both sides. Now that will cancel over here, leaving me with x is equal to 3, and this represents my domain restriction. So I know that my domain is now x such that x cannot be equal to 3 because that would make my denominator 0. X cannot be equal to 3 because that would make my denominator 0. So this is our domain. Let's go ahead and write this in lowest terms. So taking another look at my function here, f of x is equal to x squared plus 9 divided by x minus 3. Remember, we want to fully factor both the top and the bottom of our fraction. But looking at the top here, x squared plus 9 is actually not going to factor any further. It's just going to remain x squared plus 9. Now our denominator also cannot be factored any further. It's just x minus 3. So this is actually already in lowest terms, x squared plus 9 divided by x minus 3. So I don't need to do anything. I don't need to cancel anything out with my function. And this is my function in lowest terms. Thanks for watching, and I'll see you in the next video.

5. Rational Functions

Introduction to Rational Functions

College Algebra5. Rational FunctionsIntroduction to Rational Functions

Multiple Choice

Find the domain of the rational function. Then, write it in lowest terms.
$f\left(x\right)=\frac{x^2+9}{x-3}$

{x∣x≠0}, $f\left(x\right)=\frac{1}{x-3}$

{x∣x≠3}, $f\left(x\right)=\frac{x^2+9}{x-3}$

{x∣x≠−3}, $f\left(x\right)=\frac{x^2+9}{x-3}$

{x∣x≠3}, $f\left(x\right)=x+3$

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Find the domain of the rational function. Then, write it in lowest terms.
$f\left(x\right)=\frac{x^2+9}{x-3}$

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing

Find the domain of the rational function. Then, write it in lowest terms. ﻿f(x)=x2+9x−3f\left(x\right)=\frac{x^2+9}{x-3}f(x)=x−3x2+9​﻿

Find the domain of the rational function. Then, write it in lowest terms.
$f\left(x\right)=\frac{x^2+9}{x-3}$