How do you solve \frac { v + 5} { v } = \frac { 1} { 2} + \frac { 1} { 6v }v+5v=12+16v?

2 Answers
Carl S.
Apr 25, 2018

v = -29/3v=−293

Explanation:

{v+5}/v = 1/2 + 1/{6v}v+5v=12+16v

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

v+5 = v/2 + 1/6v+5=v2+16

Rearrange:

v-v/2 = 1/6-5v−v2=16−5

{2v-v}/2 = 1/6-52v−v2=16−5

v/2 = 1/6-5v2=16−5

v = 2(1/6-5)v=2(16−5)

v = (1/3-10)v=(13−10)

v = (1/3-30/3)v=(13−303)

v = -29/3v=−293

EZ as pi
Apr 25, 2018

v =-29/3 = -9 2/3v=−293=−923

Explanation:

(v+5)/v = 1/2+1/(6v)v+5v=12+16v

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)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

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