Question
upstudy study bank question image url

\( \begin{array}{ll}1.3 & \text { Given: } \\ \begin{array}{ll}\frac{x^{2}-x-6}{3 x-9} \\ 1.3 .1 & \text { For which value(s) of } x \text { will the expression be undefined? } \\ 1.3 .2 & \text { Simplify the expression fully. }\end{array}\end{array} \)

Ask by Page Edwards. in South Africa
Mar 08,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The expression is undefined when \(x=3\), and it simplifies to \(\frac{x+2}{3}\).

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

The Deep Dive

The expression will be undefined where the denominator is equal to zero. For \(3x - 9 = 0\), solving for \(x\) gives \(x = 3\). Thus, the expression is undefined at \(x = 3\). To simplify the expression \(\frac{x^{2}-x-6}{3x-9}\), first factor both the numerator and the denominator. The numerator \(x^{2}-x-6\) factors to \((x-3)(x+2)\), and the denominator \(3x-9\) factors to \(3(x-3)\). Canceling the common factor of \(x-3\) results in the simplified expression \(\frac{x+2}{3}\) for \(x \neq 3\).

Related Questions

Latest Algebra Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy