How do you solve #\frac { 2} { \sqrt { x } } = 3\sqrt { x }#?

1 Answer
Nov 23, 2017

See a solution process below:

Explanation:

First, ultiply each side of the equation by #color(red)(sqrt(x))# to eliminate the fraction and eliminate the radical while keeping the equation balanced:

#color(red)(sqrt(x)) xx 2/sqrt(x) = color(red)(sqrt(x)) xx 3sqrt(x)#

#cancel(color(red)(sqrt(x))) xx 2/color(red)(cancel(color(black)(sqrt(x)))) = 3sqrt(x)color(red)(sqrt(x))#

#2 = 3x#

Now, divide each side of the equation by #color(red)(3)# to solve for #x# while keeping the equation balanced:

#2/color(red)(3) = (3x)/color(red)(3)#

#2/3 = (color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3))#

#2/3 = x#

#x = 2/3#