how to solve this problem for v?

-3v / v-2 = -24 / v∧2-4v+4

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  • 9 years ago
    Favorite Answer

    cross multiply

    you get -3v(v∧2-4v+4) = -24(v-2)

    divide both sides by -3

    ==> v(v∧2-4v+4) = 8(v-2)

    ==> v^3 - 4v^2 +4v = 8v - 16

    ==>v^3 - 4v^2 +4v - 8v +16 = 0

    ==> v^3 - 4v^2 - 4v +16 = 0

    now solve using calculator or factor theorem

    let f(v) = v^3 - 4v^2 - 4v +16

    try f(2), it = 2^3 - 4(2^2) - 4(2) +16 = 0

    one of the solutions is v = 2

    for others, divide f(v) by the factor you just got, (v-2)

    v-2) v^3 - 4v^2 - 4v +16 ( v^2 - 2v -8

    ----- v^3 - 2v^2

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

    -2v^2 - 4v

    -2v^2 +4v

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

    -8v + 16

    -8v+16

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

    0

    now find the zeroes for the quotient, v^2 - 2v -8

    = (v +2) ( v - 4)

    therefore the solution is v = 2, -2, 4

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  • 9 years ago

    Next time, use parentheses!

    - 3*v/(v- 2) + 24/(v^2 - 4*v + 4) = 0

    ( - 3*v*(v - 2) + 24)/(v - 2)^2 = 0

    - 3*v^2 + 6*v + 24 = 0

    3*v^2 - 6*v - 24 = 0

    v^2 - 2*v - 8 = 0

    (v - 4)*(v + 2) = 0

    v1 = 4, v2 = - 2

    v = 10

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  • 9 years ago

    -3v/(v-2)=-24/(v-2)(v-2)

    -3v=-24/(v-2)

    -3v^2+6v=-24

    3v^2-6v-24=0

    (3v+6)(v-4)=0

    V=-2 v=4

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  • 6 years ago

    5h56h5h

    Source(s): t54g
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  • Anonymous
    6 years ago

    23434gf

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