How do you solve #1/x + 1/2x = 1/6 #?

2 Answers
Jun 21, 2015

Answer:

This equation has no real solutions

Explanation:

#1/x+1/2x=1/6#

First we multiply both sides by #6x# to get rid of the fractions and the unknown in the denominator:

#6+3x^2=x#
#3x^2-x+6=0#

Now we look for the solutions of a quadratic equation:

#Delta=(-1)^2-4*3*6=1-72=-71#
#Delta<0# so this equation has no real solutions.

So the base equation also has no real solutions.

Jun 21, 2015

Answer:

Is there a formatting problem in the question?

Should it have been:

How do you solve #1/x+1/(2x)=1/6# ?

If so, #x = 9# is the solution.

Explanation:

Assuming the problem is:

How do you solve #1/x+1/(2x)=1/6# ?

Multiply both sides by #6x# to get:

#6+3 = x#

So #x=9#