Question

How do you solve `(1/4)+(1/x)=(1/3)`?

Answer 1

See a solution process below:

Explanation:

First, we can multiply each side of the equation by `color(red)(12)color(blue)(x)` to eliminate the fractions while keeping the equation balanced. `color(red)(12)color(blue)(x)` is the Least Common Denominator for the three fractions:

`color(red)(12)color(blue)(x)((1/4) + (1/x)) = color(red)(12)color(blue)(x) xx (1/3)`

`(color(red)(12)color(blue)(x) xx (1/4)) + (color(red)(12)color(blue)(x) xx (1/x)) = cancel(color(red)(12))4color(blue)(x) xx (1/color(red)(cancel(color(black)(3))))`

`(cancel(color(red)(12))3color(blue)(x) xx (1/color(red)(cancel(color(black)(4))))) + (color(red)(12)cancel(color(blue)(x)) xx (1/color(blue)(cancel(color(black)(x))))) = 4x`

`3x + 12 = 4x`

Now, subtract `color(red)(3x)` from each side of the equation to solve for `x` while keeping the equation balanced:

`-color(red)(3x) + 3x + 12 = -color(red)(3x) + 4x`

`0 + 12 = (-color(red)(3) + 4)x`

`12 = 1x`

`12 = x`

`x = 12`