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

3 Answers
Jul 24, 2017

-2

Explanation:

we need to clear all the denominators first.

multiply everything byx

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

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

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