How do i get rid of a square root in the numerator?

Question

The problem is sqrt (x+4) -2 / (x)

I thought you could square the x+4 (canceling the square root in the process) as long as you square what you have in your denominator. changing it to x^2. However when I'm looking at the graph of the 2 functions, they are not equal. Are my mechanics off in getting rid of the square root?

Answer 1

Multiply both sides by sqrt (x+4) + 2. That is the conjugate of the numerator.

You'll get:  {(x+4) - 4}/x[sqrt(x+4) + 2] = x/(x(sqrt(x+4) + 2)

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

ETA: no, there is no way to completely eliminate the square root. On the answer I got, you can now sub in 0 for x and find the limit to be 1/4, but yes, it's a bit of work to get there.