Question

How do you rationalize the denominator and simplify `4/ (sqrt x +1)`?

Answer 1

I found: `(4(sqrt(x)-1))/((x-1)`

Explanation:

You can multiply and divide by `sqrt(x)-1`:
`4/(sqrt(x)+1)*(sqrt(x)-1)/(sqrt(x)-1)=`
`=(4(sqrt(x)-1))/((sqrt(x))^2cancel(-sqrt(x))+cancel(sqrt(x))-1)`
`=(4(sqrt(x)-1))/((x-1)`