Question

Rationalize the denominator in each expression 1/((√(x+3)-(√x)).

Answer 1

`(√(x+3)+√(x))/(3)`

Explanation:

given expression,

`(1)/(√(x+3)-√(x))`

on rationalizing

multiplying both numerator and denominator by
`√(x+3)+√(x)`

`(1)/(√(x+3)-√(x))* (√(x+3)+√(x))/(√(x+3)+√(x))`

`(√(x+3)+√(x))/((√(x+3))^2-(√(x))^2)`

`(√(x+3)+√(x))/((x+3)-(x))`

`(√(x+3)+√(x))/(3)`