How do you solve x/(3 sqrt (2x-3)) - 1/ (sqrt (2x-3))=1/3 and find any extraneous solutions?

1 Answer
Apr 9, 2018

x=6

Explanation:

x/(3sqrt(2x-3))-1/sqrt(2x-3)=1/3

(x-3)/(3sqrt(2x-3))=1/3

x-3=sqrt(2x-3)

(x-3)^2=2x-3

x^2-6x+9=2x-3

x^2-8x+12=0

(x-2)*(x-6)=0

So x_1=2, x_2=6. But x=2 is extraneous solution. Hence x=6 is solution of this equation.