A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

What is the simplified form of 4x^2-25/2x-5?

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Michele_Laino

  2. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    hint: we can factorize the numerator as follows: \[\Large \frac{{4{x^2} - 25}}{{2x - 5}} = \frac{{\left( {2x - 5} \right)\left( {2x + 5} \right)}}{{2x - 5}} = ...?\]

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2x+5

  4. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    since in general we have: \[\Large {a^2}{x^2} - {b^2} = \left( {ax - b} \right)\left( {ax + b} \right)\]

  5. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that's right!

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    What would the restriction be?

  7. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    since we can not divide by zero, then we have to exclude those values of x such that: \[\Large 2x - 5 = 0\]

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So -5/2

  9. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    we have to exclòude x=5/2

  10. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    exclude*

  11. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So I was wrong when I said -5/2?

  12. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes! since \[2x - 5 = 0\] when: x=5/2

  13. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    please try to solve that equation: 2x-5=0

  14. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok! I see! So the answer would be 2x+5, with a restriction of 5/2

  15. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that's right!

  16. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    :)!!! May I ask another?

  17. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok!

  18. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    What is the simplifed form of |dw:1437058472772:dw|

  19. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    here we can write your division, as a multiplication of the first fraction, times the inverse of the second fraction, like below: \[\Large \begin{gathered} \frac{{x + 1}}{{{x^2} + x - 6}}:\frac{{{x^2} + 5x + 4}}{{x - 2}} = \hfill \\ \hfill \\ = \frac{{x + 1}}{{{x^2} + x - 6}} \cdot \frac{{x - 2}}{{{x^2} + 5x + 4}} \hfill \\ \end{gathered} \]

  20. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes!

  21. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now we have to factorize the subsequent polynomials: \[\Large \begin{gathered} {x^2} + x - 6 \hfill \\ {x^2} + 5x + 4 \hfill \\ \end{gathered} \]

  22. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    (x+2)(x-3) for the first one

  23. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok! correct!

  24. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    (x+1)(x+4) for the second one

  25. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sorry, for first trinomial I got this: \[{x^2} + x - 6 = \left( {x - 2} \right)\left( {x + 3} \right)\]

  26. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    whoops yes:) you are right!

  27. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so, substituting our factorizations, in our computation, we get: \[\Large \begin{gathered} \frac{{x + 1}}{{{x^2} + x - 6}}:\frac{{{x^2} + 5x + 4}}{{x - 2}} = \hfill \\ \hfill \\ = \frac{{x + 1}}{{{x^2} + x - 6}} \cdot \frac{{x - 2}}{{{x^2} + 5x + 4}} = \hfill \\ \hfill \\ = \frac{{x + 1}}{{\left( {x - 2} \right)\left( {x + 3} \right)}} \cdot \frac{{x - 2}}{{\left( {x + 1} \right)\left( {x + 4} \right)}} = ...? \hfill \\ \hfill \\ \end{gathered} \]

  28. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1/(x+3)(x+4)

  29. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that's right!

  30. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Last one?

  31. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok!

  32. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Robin can mow a lawn in 3 hours, while Brady can mow the same lawn in 4 hours. How many hours would it take for them to mow the lawn together?

  33. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    a. 7/12 b. 12/7 c. 12 d. 7

  34. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If I call with W the work to be done, then the working rate of Robin is W/3, whereas the working rate of Brady is W/4

  35. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes:)

  36. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now, when Robin and brady work together, then the working rate is: \[\Large \frac{W}{3} + \frac{W}{4}\]

  37. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Brady*

  38. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so, we can write this equation: \[\Large \left( {\frac{W}{3} + \frac{W}{4}} \right)t = W\] where t is the requested time

  39. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I understand! Continue:) And then find like denominators

  40. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    after a simplification at the left side, we can write: \[\Large \frac{{4W + 3W}}{{12}}t = W\]

  41. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    please continue

  42. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    4x/12

  43. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    hint: we can simplify the left side, so we get: \[\Large \frac{{7W}}{{12}}t = W\]

  44. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    :) Would that be the answer?

  45. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no, please we can simplify further that equation, and we get this: \[\Large \frac{7}{{12}}t = 1\]

  46. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now I multiply both sides by 12: |dw:1437059913299:dw|

  47. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    OH! Lol I'm sorry! I must have missed that.

  48. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    12/7 ?

  49. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that's right!

  50. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yay!!

  51. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    :)

  52. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.