Question

How do you solve `\frac{3}{x} - \frac{1}{3x} = \frac{2}{3}`?

Answer 1

See the entire solution process below:

Explanation:

First, multiple each side of the equation by `color(red)(3x)` to eliminate the fractions and keep the equation balanced:

`color(red)(3x)(3/x - 1/(3x)) = color(red)(3x) xx 2/3`

`(color(red)(3x) xx 3/x) - (color(red)(3x) xx 1/(3x)) = color(red)(3x) xx 2/3`

`(color(red)(3)cancel(color(red)(x)) xx 3/color(red)(cancel(color(black)(x)))) - (cancel(color(red)(3)color(red)(x)) xx 1/color(red)(cancel(color(black)(3x)))) = cancel(color(red)(3))color(red)(x) xx 2/color(red)(cancel(color(black)(3)))`

`(3 xx 3) - 1 = (x xx 2)`

`9 - 1 = 2x`

`8 = 2x`

Now, divide each side of the equation by `color(red)(2)` to solve for `x` while keeping the equation balanced:

`8/color(red)(2) = (2x)/color(red)(2)`

`4 = (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2))`

`4 = x`

`x = 4`