Matematika

Pertanyaan

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1 Jawaban

  • a) ( a / 2) + ( a-4 / 3 )

    = a ( 3) + 2(a - 4)
    --------------------------
    ( 2 ) ( 3)

    = 3a + 2a - 8
    --------------------
    6

    = 5a - 8
    -------------
    6

    b) ( 4 / y ) - ( 4 / y-2 )

    = 4(y - 2) - 4 ( y )
    --------------------------
    y ( y - 2)

    = 4y - 8 - 4y
    -----------------
    y² - 2y

    = - 8
    --------
    y² - y

    c) ( 4 / p+3 ) - ( 3 / p-2 )

    = 4 ( p - 2) - 3(p + 3)
    ------------------------------
    ( p + 3) ( p - 2)

    = 4p - 8 - 3p - 9
    ------------------------
    p² + 3p - 2p - 6

    = p - 17
    --------------
    p² + p - 6

    d) ( 3b-2 / 6 ) - ( b+4 / 3 )

    = 3 ( 3b - 2) - 6 ( b + 4)
    ---------------------------------
    ( 6 )( 3)

    = 9b - 6 - 6b - 24
    --------------------------
    18

    = 3b - 30
    --------------
    18

    = 3( b - 10)
    -----------------
    3 ( 6)

    = b - 10
    ------------
    6

    e) ( 5 / a+b ) + ( 2 / a-b )

    = 5 ( a - b ) + 2 ( a + b )
    ---------------------------------
    ( a + b ) ( a - b )

    = 5a - 5b + 2a + 2b
    -----------------------------
    a² - ab + ab - b²

    = 7a - 3b
    --------------
    a² - b²

    f) ( 4+x / x²-9 ) - ( 2 / x+3 )

    = ( 4 + x )( x + 3) - 2(x² - 9)
    ---------------------------------------
    ( x² - 9 )( x + 3)

    = 4x + x² + 12 + 3x - 2x² + 18
    -----------------------------------------
    ( x² - 9)( x + 3)

    = - x² + 7x + 30
    ------------------------
    ( x² - 9)( x + 3)

    = ( - x + 10)( x + 3)
    ---------------------------
    ( x² - 9)(x + 3)

    = (- x + 10)
    ----------------
    ( x² - 9 )