How do you solve #\frac { v + 5} { v } = \frac { 1} { 2} + \frac { 1} { 6v }#?

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Answer 1 · 2018-04-25T06:22:16

#v = -29/3#

#{v+5}/v = 1/2 + 1/{6v}#

Multiply everything by #v# (since it's not zero, as it is a divisor in the expression)

#v+5 = v/2 + 1/6#

Rearrange:

#v-v/2 = 1/6-5#

#{2v-v}/2 = 1/6-5#

#v/2 = 1/6-5#

#v = 2(1/6-5)#

#v = (1/3-10)#

#v = (1/3-30/3)#

#v = -29/3#

Answer 2 · 2018-04-25T07:14:01

#v =-29/3 = -9 2/3#

#(v+5)/v = 1/2+1/(6v)#

If you have an equation which has fractions you can get rid of them by multiplying every term by the LCD which in this case is #color(blue)(6v)#

#(color(blue)(6cancelv)xx(v+5))/cancelv = (color(blue)(cancel6^3v)xx1)/cancel2+(color(blue)(cancel(6v))xx1)/cancel(6v)" "larr# cancel

#6(v+5) =3v+1" "larr# no fractions!! Solve for #v#

#6v+30 =3v+1#

#6v-3v = 1-30#
#3v = -29#
#v =-29/3 = -9 2/3#