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

2 Answers
Apr 25, 2018

v = -29/3

Explanation:

{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

Apr 25, 2018

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

Explanation:

(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