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anonymous

  • one year ago

What is the simplified form of x plus 2 over x squared minus 3x minus 10 • x minus 3 over x squared plus x minus 12 ? 1 over the quantity x minus 3 times the quantity x plus 4 1 over the quantity x minus 3 times the quantity x plus 2 1 over the quantity x plus 4 times the quantity x minus 5 1 over the quantity x plus 2 times the quantity x minus 5

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  1. anonymous
    • one year ago
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    \[\frac{ x + 2 }{ x^2 - 3x - 10 } \times \frac{ x - 3 }{ x^2 + x -12 }\]

  2. anonymous
    • one year ago
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    @iGreen do i flip the 2nd fraction then horizontally multiply ?

  3. iGreen
    • one year ago
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    No, that was for division..you can horizontally multiply now.

  4. anonymous
    • one year ago
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    oh okay

  5. anonymous
    • one year ago
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    quick question when we horizontally multipl would the numerator be x^2 + 2 -3 or x+ 2 x- 3?

  6. iGreen
    • one year ago
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    None.. \(\sf (x+2)(x-3)\) x * x = ? x * -3 = ? 2 * x = ? 2 * -3 = ?

  7. anonymous
    • one year ago
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    x^2 -3x 2 -6

  8. iGreen
    • one year ago
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    Actually, first we cancel the common factors.

  9. anonymous
    • one year ago
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    for the denominator ?

  10. iGreen
    • one year ago
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    For the 2nd fraction

  11. iGreen
    • one year ago
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    1st*

  12. iGreen
    • one year ago
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    Factor \(\sf x^2 - 3x - 10\) from the numerator..tell me what you get.

  13. iGreen
    • one year ago
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    Can you do that?

  14. anonymous
    • one year ago
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    is it x/ x^2 - 3x -5

  15. iGreen
    • one year ago
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    No..

  16. iGreen
    • one year ago
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    Can you factor \(\sf x^2 - 3x - 10\)?

  17. anonymous
    • one year ago
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    oh yeah give me sec

  18. iGreen
    • one year ago
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    Okay

  19. anonymous
    • one year ago
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    (x + 2) (x - 5)

  20. iGreen
    • one year ago
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    Yes, so we have: \(\sf \dfrac{x+2}{(x-5)(x+2)} \times \dfrac{x-3}{x^2+x-12}\) The x + 2's cancel out, giving us: \(\sf \dfrac{\cancel{x+2}}{(x-5)(\cancel{x+2})} \times \dfrac{x-3}{x^2+x-12}\) \(\sf \dfrac{1}{(x-5)} \times \dfrac{x-3}{x^2+x-12}\)

  21. iGreen
    • one year ago
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    Now we multiply horizontally..but first factor \(\sf x^2 + x - 12\).

  22. anonymous
    • one year ago
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    (x - 3) (x + 4)

  23. anonymous
    • one year ago
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    but it would be \[\frac{ 1 }{ (x - 5) } \times \frac{ 1 } { ( x + 4)}\]

  24. iGreen
    • one year ago
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    Yes..which gives us: \(\sf \dfrac{1}{(x-5)(x+4)}\)

  25. iGreen
    • one year ago
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    @shinebrightlikeadimon

  26. anonymous
    • one year ago
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    okay thanks so much for some reason i lost connection thats why im replying late

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