Question

How do you solve `2/8=(n+4)/(n-4)`?

Answer 1

See a solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(8)color(blue)((n - 4))` to eliminate the fractions while keeping the equation balanced:

`color(red)(8)color(blue)((n - 4)) xx 2/8 = color(red)(8)color(blue)((n - 4)) xx (n + 4)/(n - 4)`

`cancel(color(red)(8))color(blue)((n - 4)) xx 2/color(red)(cancel(color(black)(8))) = color(red)(8)cancel(color(blue)((n - 4))) xx (n + 4)/color(blue)(cancel(color(black)(n - 4)))`

`2(n - 4) = 8(n + 4)`

Next, we expand the term in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

`color(red)(2)(n - 4) = color(blue)(8)(n + 4)`

`(color(red)(2) * n) - (color(red)(2) * 4) = (color(blue)(8) * n) + (color(blue)(8) * 4)`

`2n - 8 = 8n + 32`

Then, subtract `color(red)(2n)` and `color(blue)(32)` from each side of the equation to isolate the `n` term while keeping the equation balanced:

`-color(red)(2n) + 2n - 8 - color(blue)(32) = -color(red)(2n) + 8n + 32 - color(blue)(32)`

`0 - 40 = (-color(red)(2) + 8)n + 0`

`-40 = 6n`

Now, divide each side of the equation by `color(red)(6)` to solve for `n` while keeping the equation balanced:

`-40/color(red)(6) = (6n)/color(red)(6)`

`-20/3 = (color(red)(cancel(color(black)(6)))n)/cancel(color(red)(6))`

`-20/3 = n`

`n = -20/3`