Question

How do you solve `(x-1)/x + 7/(3x) = 9/(4x)`?

Answer 1

`x = 11/12`

Explanation:

Multiply both sides by `12x`, (the LCM of x, 3x and 4x)

`12(x - 1) + 7*4 = 9*3`
`12x - 12 + 28 = 27`

Isolate the x

`12x - 12 = 27 - 28`
`12x - 12 = -1`
`12x = -1+12`
`x = 11/12`

Check if the answer doesn't cause an absurd, in this case,
`x != 0`
`3x != 0 rarr x != 0`
`4x != 0 rarr x!= 0`

So the answer is valid.