Simplify and reduce to lowest terms:?

1. ( 4x³y ) / ( 2x²y )

2. 1 / x + 4

3. 1 / ( x + 5y ) – 5 ? ( x – 5y) + 3 / ( x² - 25y² )

4. [ ( x³ + 27) / ( x + 3 ) ] / [ ( x² - 3x + 9 ) / ( x – 3 ) ]

5. (w / 45) + [ ( 3w + 2 ) / 30 ]

6. [ 1 / ( 10a³b ) ] + [ 4 / (ac³ ) ]

1 Answer

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  • M
    Lv 6
    1 decade ago
    Favorite Answer

    1. ( 4x³y ) / ( 2x²y ) = 2x

    2. 1/x + 4 = 1/x + 4x/x = (1+4x) / x

    3. 1 / (x + 5y) – 5/(x – 5y) + 3/(x² - 25y²) =

    1/(x + 5y) – 5/(x – 5y) + 3/(x + 5y)(x - 5y) =

    [(x – 5y) - 5(x + 5y) + 3] / (x + 5y)(x- 5y) =

    [x – 5y - 5x - 25y + 3] / (x + 5y)(x- 5y) =

    [-4x – 30y + 3] / (x + 5y)(x- 5y)

    4. [(x³ + 27)/(x + 3)] / [(x² - 3x + 9)/(x – 3)] =

    [(x³ + 27)/(x + 3)] · [(x – 3)/(x² - 3x + 9)] =

    [(x + 3)(x² - 3x + 9)/(x + 3)] · [(x – 3)/(x² - 3x + 9)] =

    (x² - 3x + 9)·(x – 3)/(x² - 3x + 9) =

    x – 3

    5. (w / 45) + [ (3w + 2)/30 ]

    45 = 3·15, 30 = 2·15 => common denominator = 2·3·15 = 90

    2w/90 + 3·(3w + 2)/90 =

    [2w + 3·(3w + 2)] / 90 =

    [2w + 9w + 6] / 90 =

    [11w + 6] / 90

    6. [ 1/(10a³b) ] + [ 4/(ac³·) ]

    common denominator 10a³bc³

    [ 1·c³/(10a³b·c³) ] + [ 4·10a²b / (ac³·10a²b) ] =

    (c³ + 40a²b) / 10a³bc³

    Hope this helps

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