# how to solve this problem for v?

-3v / v-2 = -24 / v∧2-4v+4

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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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• 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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• -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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• 5h56h5h

Source(s): t54g
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