Question

How do you solve `3/(4x)-1/2=2/(3x)-2` and check for extraneous solutions?

Answer 1

`x = -1/18`

Explanation:

`3/(4x)-1/2=2/(3x)-2" "x!=0`

The biggest problem is the fractions. Multiply by the LCM to cancel the denominators. LCM = `12x`

`(color(red)(12x xx)3)/(4x)-(color(red)(12x xx)1)/2=(color(red)(12x xx)2)/(3x)-(color(red)(12x xx)2)`

`(color(red)(cancel(12x)^3 xx)3)/cancel(4x)-(color(red)(cancel(12)^6x xx)1)/cancel2=(color(red)(cancel(12x)^4 xx)2)/(cancel(3x))-(color(red)(12x xx)2)`

`9 -6x = 8 -24x`

`24x-6x = 8-9`

`18x = -1`

`x = -1/18`