How do you rationalize the denominator and simplify #[(x+3)^(1/2)-(x)^(1/2)] / 3#?

1 Answer
Jan 27, 2018

Answer:

#((x+3)^(1/2)-(x)^(1/2))/3=1/((x+3)^(1/2)+(x)^(1/2))#

Explanation:

The denominator is a natural number and it appears as you wanted to rationalize numerator. This is done as follows:

#((x+3)^(1/2)-(x)^(1/2))/3#

= #((x+3)^(1/2)-(x)^(1/2))/3xx((x+3)^(1/2)+(x)^(1/2))/((x+3)^(1/2)+(x)^(1/2))#

= #((x+3)-(x))/(3((x+3)^(1/2)+(x)^(1/2)))#

= #3/(3((x+3)^(1/2)+(x)^(1/2)))#

= #1/((x+3)^(1/2)+(x)^(1/2))#