Question

How do you solve `\frac { 3} { n } = \frac { 6} { n - 4}`?

Answer 1

See a solution process below:

Explanation:

Multiply each side of the equation by the lowest common denominator, which is `(color(red)(n)(color(blue)((n - 4)))`, to eliminate the fractions while keeping the equation balanced:

`3/n xx color(red)(n)(color(blue)(n - 4)) = 6/(n - 4) xx color(red)(n)color(blue)((n - 4))`

`3/color(red)(cancel(color(black)(n))) xx cancel(color(red)(n))(color(blue)(n - 4)) = 6/color(blue)(cancel(color(black)((n - 4)))) xx color(red)(n)cancel(color(blue)((n - 4)))`

`3(n - 4)= 6n`

Next, expand the terms in parenthesis on the left side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

`3(n - 4)= 6n`

`(3 xx n) - (3 xx 4)= 6n`

`3n - 12 = 6n`

Then, subtract `color(red)(3n)` from each side of the equation to isolate the `n` term while keeping the equation balanced:

`-color(red)(3n) + 3n - 12 = -color(red)(3n) + 6n`

`0 - 12 = (-color(red)(3) + 6)n`

`-12 = 3n`

Now, divide each side of the equation by `color(red)(3)` to solve for `n` while keeping the equation balanced:

`-12/color(red)(3) = (3n)/color(red)(3)`

`-4 = (color(red)(cancel(color(black)(3)))n)/cancel(color(red)(3))`

`-4 = n`

`n = -4`