Question
upstudy study bank question image url

\( \begin{aligned} \text { 5. } \frac{m^{2}+7 m}{3 m} \div \frac{49-m^{2}}{3 m-21} & = \\ & = \\ & =\end{aligned} \)

Ask by Murphy Whittaker. in Thailand
Mar 16,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The result of the expression is -1.

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

Mind Expander

To solve the problem, start by simplifying the expression step by step. First, let's rewrite the equation: \[ \frac{m^{2}+7 m}{3 m} \div \frac{49-m^{2}}{3 m-21} \] Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{m^{2}+7 m}{3 m} \times \frac{3 m - 21}{49 - m^{2}} \] Now, factor the parts of the fractions. The numerator of the first fraction can be factored as: \[ m(m + 7) \] The denominator \(3m - 21\) can be factored as: \[ 3(m - 7) \] And notice that \(49 - m^{2}\) can be factored as: \[ (7 - m)(7 + m) \] Putting it all together: \[ \frac{m(m + 7)}{3m} \times \frac{3(m - 7)}{(7 - m)(7 + m)} \] Cancelling \(3m\) in the first part gives us: \[ \frac{m + 7}{3} \times \frac{3(m - 7)}{(7 - m)(7 + m)} \] Now, notice that \(7 - m\) can be factored as \(-1(m - 7)\): \[ \frac{m + 7}{3} \times \frac{3(-1)(m - 7)}{-(m + 7)(m - 7)} \] Next, the \(3\) cancels and we can simplify further. The final simplified expression becomes: \[ \frac{1(m - 7)}{1} = m - 7 \] So the answer to the expression is: \[ \boxed{m - 7} \]

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