Question

How do you solve for x in the simplest radical form for `(x^2+2x+4)/x =(2x)/1`?

Answer 1

If `a/b=c/d->a*d=b*c` this is called cross-product.

Applying this, we have:

`(x^2+2x+4)*1=x*2x->`

`x^2+2x+4=2x^2->`

Subtract `2x` on both sides and multiply by `-1`

`x^2-2x-4=0`

There are several ways to solve this. I will rewrite for the square:

`(x^2-2x+1)-5=0->`
`(x-1)^2-5=0->`
`(x-1)^2=5->`
`x-1=+sqrt5or-sqrt5->`

Solution:

`x=1+sqrt5orx=1-sqrt5`