Give the quotient in simplest form.?

3x^2-xy-2y^2 / x^3-y^3 / 15x^2+10xy/ 5x^2-5xy+5y^2

It's 3x squared - xy- 2ysquared divided by x cube- y cube then divide the quotient of 15xsquared+10xy and 5xsquared-5xy+5ysquared.

Please help

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  • 1 decade ago
    Favorite Answer

    3x^2-xy-2y^2 / x^3-y^3

    = [(3x+2y)(x-y)] / [(x-y)(x^2+xy+y^2)]

    = (3x+2y) / (x^2+xy+y^2)

    15x^2+10xy/ 5x^2-5xy+5y^2

    = [5x(3x+2y)]/[5(x^2-xy+y^2)]

    = [x(3x+2y)]/(x^2-xy+y^2)

    => [(3x+2y) / (x^2+xy+y^2)] / [x(3x+2y)]/(x^2-xy+y^2)

    = (x^2-xy+y^2)/ [x(x^2+xy+y^2)]

    QED

  • 1 decade ago

    Joelle, the trick here is to factor the expressions as best you can, then cancell the common factors and maybe multiply out the result.

    So yo can write...

    3x^2 -xy -2y^2 = (3x+2y)(x-y),

    x^3-y^3 = (x-y)(x^2+xy+y^2)

    this pair simplifies to (3x+2y)/)(x^2+xy+y^2)

    15x^2+10xy=5x(3x+2y)

    5x^2-5xy+5y^2=5(x^2-xy+y^2)

    you should see that this pair simplifies to

    x(3x+2y) / (x^2-xy+y^2)

    now when you do the next division, the term (3x+2y) also vanishes so that i get

    (x^2-xy+y^2)/(x(x^2+xy+y^2))

    hth

  • Anonymous
    1 decade ago

    3x^2-xy-2y^2 / x^3-y^3 / 15x^2+10xy/ 5x^2-5xy+5y^2

    let:

    A = 3x^2-xy-2y^2 =(x-y)(2y+3x)

    B = x^3-y^3 = (x-y)(x^2+xy+y^2)

    C =15x^2+10xy =5x(3x+2y)

    D = 5x^2-5xy+5y^2 =5(x^2-xy+y^2)

    This is A/B/C/D = (A/B) / (C/D) =

    (AD)/(BC) = (A/B)*(D/C)

    A/B = (x-y)(2y+3x) / {(x-y)(x^2+xy+y^2)} = (2y+3x) / (x^2+xy+y^2)

    D/C = 5(x^2-xy+y^2) / {5x(3x+2y)} =

    {(x^2-xy+y^2) /{x(3x+2y)}

    (A/B)*(D/C) = {(2y+3x) / (x^2+xy+y^2)}*{(x^2-xy+y^2) /{x(3x+2y)} =

    (x^2-xy+y^2) / {x(x^2+xy+y^2)}

    Summary:

    3x^2-xy-2y^2 / x^3-y^3 / 15x^2+10xy/ 5x^2-5xy+5y^2 =

    (x^2-xy+y^2) / {x(x^2+xy+y^2)}

  • 1 decade ago

    { ( 3x + 2y ) ( x - y ) } / { ( x - y ) ( x^2 + xy + y^2 ) }

    - all over -

    { 5x ( 3x + 2y ) } / { 5 ( x^2 - xy + y^2 ) }

    5 ( 3x + 2y ) ( x - y ) ( x^2 - xy + y^2 )

    - over -

    5x ( x - y ) ( x^2 + xy + y^2 ) ( 3x + 2y )

    cancel 5, (3x+2y) and (x-y)

    giving you:

    x^2 - xy + y^2

    -all over-

    x^2 + xy + y^2

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  • Anonymous
    4 years ago

    cube root 162 cube root 2 * cube root 2 cube root 648 6 cube root 3 --------------------------------------... ============== cube root 2 cube root 2 * cube root 2= cube root 8= 2 ans 3 cube root 3

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