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sloppycanada

  • one year ago

How would one go about solving the following rational functions?

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  1. sloppycanada
    • one year ago
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    |dw:1435629520612:dw|

  2. anonymous
    • one year ago
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    Equals what again ?

  3. sloppycanada
    • one year ago
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    -2

  4. sloppycanada
    • one year ago
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    @AngusV

  5. SolomonZelman
    • one year ago
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    Can you draw your function a little better, please? I can see the left hand side of the equation, \(\large\color{black}{ \displaystyle \frac{5}{5-p}-\frac{p^2}{5-p} }\) but what is this equal to? What is the right side of your equation?

  6. sloppycanada
    • one year ago
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    |dw:1435631324555:dw|

  7. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle \frac{5}{5-p}-\frac{p^2}{5-p}=-2}\) combine the two fractions first

  8. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle \frac{5-p^2}{5-p}=-2}\) would this be correct, how do you think?

  9. sloppycanada
    • one year ago
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    No this wouldn't be correct? Since -p - (-p) would cancel out right?

  10. SolomonZelman
    • one year ago
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    it is correct

  11. SolomonZelman
    • one year ago
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    just as \(\large\color{black}{ \displaystyle \frac{A}{B}-\frac{C}{B}\Rightarrow \frac{A-C}{B}}\) so is \(\large\color{black}{ \displaystyle \frac{5}{5-p}-\frac{p^2}{5-p}\Rightarrow \frac{5-p^2}{5-p}}\)

  12. SolomonZelman
    • one year ago
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    is this making sense?

  13. sloppycanada
    • one year ago
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    Oh okay.. so then I multiply both sides by the denominator?

  14. SolomonZelman
    • one year ago
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    yes, you need to multiply times 5-p on both sides

  15. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle \frac{5-p^2}{5-p}=-2}\) \(\large\color{black}{ \displaystyle \left(\frac{5-p^2}{5-p}\right)\times (5-p)=-2 \times (5-p)}\)

  16. SolomonZelman
    • one year ago
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    5-p on the left side cancels \(\large\color{black}{ \displaystyle 5-p^2=-2(5-p)}\)

  17. SolomonZelman
    • one year ago
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    now, solve for p

  18. sloppycanada
    • one year ago
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    5 - p^2 = -10 + 2p?

  19. SolomonZelman
    • one year ago
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    yes

  20. SolomonZelman
    • one year ago
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    now, bring everything over to the left side

  21. SolomonZelman
    • one year ago
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    or, you can subtract 2p from both sides, subtract 5 from both sides, divide by -1 on both sides, and complete the square

  22. sloppycanada
    • one year ago
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    5-p^2 + 10 - 2p = 0 15p-p^2 -2p

  23. SolomonZelman
    • one year ago
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    15p?

  24. sloppycanada
    • one year ago
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    Sorry 15 - p^2

  25. SolomonZelman
    • one year ago
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    where is -2p though?

  26. SolomonZelman
    • one year ago
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    should be: -p²-2p+15=0

  27. sloppycanada
    • one year ago
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    15 - p^2 - 2p = 0?

  28. sloppycanada
    • one year ago
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    oh okay

  29. SolomonZelman
    • one year ago
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    yes, in my order is going to be more convenient

  30. SolomonZelman
    • one year ago
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    -p²-2p+15=0 divide both sides by -1, and factor the left side

  31. sloppycanada
    • one year ago
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    wait -5 or 3

  32. SolomonZelman
    • one year ago
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    you mean the numbers to factor, or solutions for p?

  33. SolomonZelman
    • one year ago
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    p²+2p-15=0 (p-3)(p+5)=0 so that we have +2p, and yet -15.

  34. SolomonZelman
    • one year ago
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    now p=?

  35. sloppycanada
    • one year ago
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    p = 3 and -5

  36. sloppycanada
    • one year ago
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    or, sorry I meant or.

  37. SolomonZelman
    • one year ago
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    yes p=3, p=-5.

  38. SolomonZelman
    • one year ago
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    this is the original prob, correct?

  39. sloppycanada
    • one year ago
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    Yes.

  40. SolomonZelman
    • one year ago
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    yw

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