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20 December, 19:49

Simplify completely the quantity x squared plus x minus 12 over quantity x squared minus x minus 20 divided by the quantity 3 x squared minus 24 x plus 45 over quantity 12 x squared minus 48 x minus 60.

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  1. 20 December, 19:59
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    X² + x - 12 / x² - x - 20 : 3x² - 24x + 45 / 12x² - 48x - 60

    x² + x - 12 / x² - x - 20 * 12x² - 48x - 60 / 3x² - 24x + 45

    (x² + x - 12) (12x² - 48x - 60)

    (x² - x - 20) (3x² - 24x + 45)

    12x^4 - 48x³ - 60x² + 12x³ - 48x² - 60x - 144x² + 576x + 720

    3x^4 - 24x³ + 45x² - 3x³ + 24x² - 45x - 60x² + 480x - 900

    12x^4 - 48x³ + 12x³ - 60x² - 48x² - 144x² - 60x + 576x + 720

    3x^4 - 24x³ - 3x³ + 45x² + 24x² - 60x² - 45x + 480x - 900

    12x^4 - 36x³ - 252x² + 516x + 720

    3x^4 - 27x³ + 9x² + 435x - 900

    12 (x^4 - 3x³ - 21x² + 43x + 60)

    3 (x^4 - 9x³ + 3x² + 145x + 300)

    4 (x^4 - 3x³ - 21x² + 43x + 60)

    (x^4 - 9x³ + 3x² + 145x + 300)
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