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

Question

Eli Assouline · Accepted Answer

#-2#

First, all of the denominators must be cleared.

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#

Savannah Anderson · Answer

#x=-2#

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#

We can combine the two terms on the right because they have the same denominator.

#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#

Hazel Anglin · Answer

#x=-2#

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

As long as you apply the same to both sides, we can do anything because we have an equation.

To cancel terms, multiply each one by the denominators' LCM.

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

The equation is now as follows:

#x+4 =2#

#x = 2-4#

#x =-2#

Julia Adams · Answer

undefined To solve the equation 1/2 + 2/x = 1/x, we can start by getting rid of the denominators. Multiply every term in the equation by the least common denominator (LCD), which is 2x. This gives us 2x(1/2) + 2x(2/x) = 2x(1/x). Simplifying each term, we have x + 4 = 2. Next, subtract 4 from both sides of the equation to isolate the variable x. This gives us x = -2. Therefore, the solution to the equation is x = -2.