Question

Write the rationalized expression of: sqrt9/sqrt3+sqrtx

Answer 1

`(3(√(3) -√(x)))/(3-x)` or
`(3√(3)-3√(x) )/(3-x)`

Explanation:

`(√(9) )/(√(3) +√(x) )`

`(3)/(√(3)+√(x) )`

Multiply by the opposite by using the difference of squares converse formula.

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

`(3(√(3) -√(x)))/(3-x)`

`(3√(3)-3√(x) )/(3-x)`

Answer 2

3 sqrt(3) - 3 sqrt(x)

---------------------------

3 - x

Explanation:

sqrt(9) = 3

so writing the expression as

3

--------------------

sqrt(3) + sqrt(x)

Multiply by the conjugate, sqrt(3) - sqrt(x) in the numerator and denominator

3 sqrt(3) - sqrt(x)

-------------------- * ------------------

sqrt(3) + sqrt(x) sqrt(3) - sqrt(x)

Foil the denominator

3 sqrt(3) - 3 sqrt(x)

---------------------------

sqrt(3) sqrt(3) + sqrt(3x) - sqrt(3x) - sqrt(x^2)

Simplify

3 sqrt(3) - 3 sqrt(x)

---------------------------

3 - x