(Please Help) Algebra problem?

Simplify: (x^3-4x)/(x^2+3x+2)

Update:

Ryan- can you show me how you get that answer

Comments

  • x³ - 4x = x(x² - 4) = x(x - 2)(x + 2)

    x² + 3x + 2 = (x + 1)(x + 2)

    => x(x - 2)(x + 2)/(x + 1)(x + 2)

    i.e. x(x - 2)/(x + 1)

    :)>

  • I wish there was a "prettier" way to show this.

    Start by factoring the numerator.

    x^3-4x = x(x^2-4) = x (x-2)(x+2)

    Next, denominator.

    (x^2+3x+2) = (x+2) (x+1).

    Lastly, remove common factors:

    x ( x -2 ) / (x + 1)

  • = (x³ - 4x) / (x² + 3x + 2) → you factorize x

    = x(x² - 4) / (x² + 3x + 2) → you know that: 4 = 2²

    = x(x² - 2²) / (x² + 3x + 2) → you recognize: a² - b² = (a + b)(a - b)

    = x(x + 2)(x - 2) / (x² + 3x + 2) → you know that: 3x = 2x + x

    = x(x + 2)(x - 2) / [x² + (2x + x) + 2] → you group

    = x(x + 2)(x - 2) / [(x² + 2x) + (x + 2)]

    = x(x + 2)(x - 2) / [x(x + 2) + (x + 2)] → you factorize (x + 2)

    = x(x + 2)(x - 2) / [(x + 2)(x + 1)] → you simplify by (x + 2)

    = x(x - 2) / (x + 1)

  • (x^3-4x)/(x^2+3x+2) =

    x(x^2-4) / (x+2)(x+1) =

    x(x+2)(x-2) / (x+2)(x+1) =

    cancel (x+2) :

    x(x-2) / (x+1)

    x can't be -1, -2

  • x (x² - 4)

    ----------------

    (x + 2)(x + 1)

    x (x - 2)(x + 2)

    -------------------

    (x + 2)(x + 1)

    x (x - 2)

    ------------

    x + 1

  • Factor the numerator and denominator:

    x ( x^2 - 4 ) ....x ( x + 2)( x - 2 )

    ----------------- = ----------------------------- .............. Cancel common factors

    x^2 + 3x + 1 .... ( x + 2 )( x + 1 )

    x ( x - 2 ) ..... x^2 - 2x

    --------------- = ---------------- THE ANSWER

    x + 1 ----------- x + 1

  • x^5+3x^4-2x^3-12x^2-8x

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