Question

How do you rationalize `12/(sqrt5-1)`?

Answer 1

To rationalize the denominator of an irrational fraction, multiply the numerator and denominator by the conjugate of the denominator.

`12/(sqrt(5)-1)`
`color(white)("XXXX")` `=2/(sqrt(5)-1) xx(sqrt(5)+1)/(sqrt(5)+1)`

`color(white)("XXXX")` `= (2sqrt(5)-2)/(5-1)`

`color(white)("XXXX")` `= (sqrt(5)-1)/2`