How do you solve `n/(n-3)=2/3`?

First, we can cross multiply to get `n` out of a fraction:
`3n=2(n-3)`

We can use the distributive property on the right-hand side:
`3n=2n-6`

By subtracting `2n` from both sides, we get `n` terms on one side:
`n=-6` which is our answer

First, multiply each side of the equation by `color(red)((n - 3))color(blue)(3)` to eliminate the fractions while keeping the equation balanced. `color(red)((n - 3))color(blue)(3)` is the Lowest Common Denominator of the two fractions:

`color(red)((n - 3))color(blue)(3) xx n/(n -3) = color(red)((n - 3))color(blue)(3) xx 2/3`

`cancel(color(red)((n - 3)))color(blue)(3) xx n/color(red)(cancel(color(black)(n - 3))) = color(red)((n - 3))cancel(color(blue)(3)) xx 2/color(blue)(cancel(color(black)(3)))`

`3n = 2(n - 3)`

Next, expand the terms in parenthesis on the right side of the equation:

`3n = (2 xx n) - (2 xx 3)`

`3n = 2n - 6`

Now, subtract `color(red)(2n)` from each side of the equation to solve for `n` while keeping the equation balanced:

`-color(red)(2n) + 3n = color(red)(2n) + 2n - 6`

`(-color(red)(2) + 3)n = 0 - 6`

`1n = -6`

`n = -6`