Question

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

Answer 1

`-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`

Answer 2

`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`

Answer 3

`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`