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

##
I know the solution to

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

is

#x=+-0.5#

At least it is the solution in my math book.

But I don't understand how you solve it.

When I tried i got #x=+-0,25# I think.

So I typed the problem into Cymath. And it tells me to do the following:

**One.** Simplify #1/x-1/(2x)# to #1/(2x)#

#1/(2x)=2x#

**Two.** Multiply both sides by #2x#

#1=2x*2x#

**Three.** Simplify #2x*2x# to #4x^2#

#1=4x^2#

**Four.** Divide both sides by #4#

#1/4=x^2#

**Five.** Take the square root of both sides.

#+-sqrt(1/4)=x#

So the answer is #x=+-0.5#

But the thing I don't understand is the first step. Why does #1/x-1/(2x)# equals to #1/(2x)# ?

It just seems so illogical to me. Is there another way to solve the equation? Or can someone please explain why this is?

I know the solution to

is

At least it is the solution in my math book.

But I don't understand how you solve it.

When I tried i got

So I typed the problem into Cymath. And it tells me to do the following:

**One.** Simplify

**Two.** Multiply both sides by

**Three.** Simplify

**Four.** Divide both sides by

**Five.** Take the square root of both sides.

So the answer is

But the thing I don't understand is the first step. Why does

It just seems so illogical to me. Is there another way to solve the equation? Or can someone please explain why this is?

##### 2 Answers

See the explanation please.

#### Explanation:

Let's continue:

Multiply both sides by

2nd method:

To get rid of denominators multiply both sides of equation by the Lowest Common Denominator (LCD) in this case

#### Explanation:

Given:

Considering the left hand side only for a moment

We need to make the bottom values (denominators) the same. Multiply by 1 and you do not change the value. However, 1 comes in many forms.

Multiply both sides by

Divide both sides by 2

Square root both sides

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Set

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