Here is my problem:


so--here's my problem which I know you all will find easy, but I can't seem to solve for some reason:

If 4- (1/x)=4x, then x=?

Here are my steps:
1. add the 1/x to the other side resulting in: 4=4x + (1/x)
2. find a common denominator for the right hand side? Is that the right thing to do?

I can't seem to get past this?

Any help will be greatly appreciated!

That'll work.

Solution below -

4=4x+1/x

4= (4x^2 +1)/x

4x = 4x^2 + 1

0 = 4x^2 - 4x + 1

0 = 4x^2 - 2x - 2x + 1

0 = 2x(2x-1) - 1(2x-1)

0 = (2x-1)^2

0 = 2x-1

1 = 2x

1/2 = x

Your steps are right.

Next step is simply to multiply everything by x.

Solve the resulting quadratic equation.