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

3 Answers
Jul 24, 2017

Answer:

#-2#

Explanation:

we need to clear all the denominators first.

multiply everything by#x#

#1/2x+2cancel(x/x)=cancel(x/x)^1#

#1/2x+2=1#

multiply everything by #2#

#2 xx 1/2x+2xx2=1xx2#

#=>x+4=2#

subtract #4#

#x+4-4=2-4#

#:.x=-2#

Jul 24, 2017

Answer:

#x=-2#

Explanation:

Our goal is to isolate the variable, #x#. Start by moving all of the #x# terms to the same side.

#1/2 = 1/x-2/x#

Since both terms on the right share the same denominator, we can combine them.

#1/2 = (1-2)/x#

Now we only have one #x# term. Cross multiply to get rid of the fractions.

#x=2(1-2)#

Solve.

#x=-2#

Jul 24, 2017

Answer:

#x=-2#

Explanation:

#1/2+2/x =1/x" "larr# LCM of denominators #=2x#

We have an equation, so we can do anything as long as you do the same to both sides.

Multiply each term by the LCM of the denominators to cancel them.

#(cancel2x xx1)/cancel2 +(2cancelx xx 2)/cancelx = (2cancelx xx 1)/cancelx#

This leaves the equation as:

#x+4 =2#

#x = 2-4#

#x =-2#