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

1 Answer
Aug 15, 2016

Answer:

#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#