How do you rationalize the denominator and simplify [(x+3)^(1/2)-(x)^(1/2)] / 3(x+3)12−(x)123?

1 Answer
Shwetank Mauria
Jan 27, 2018

((x+3)^(1/2)-(x)^(1/2))/3=1/((x+3)^(1/2)+(x)^(1/2))(x+3)12−(x)123=1(x+3)12+(x)12

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)12−(x)123

= ((x+3)^(1/2)-(x)^(1/2))/3xx((x+3)^(1/2)+(x)^(1/2))/((x+3)^(1/2)+(x)^(1/2))(x+3)12−(x)123×(x+3)12+(x)12(x+3)12+(x)12

= ((x+3)-(x))/(3((x+3)^(1/2)+(x)^(1/2)))(x+3)−(x)3((x+3)12+(x)12)

= 3/(3((x+3)^(1/2)+(x)^(1/2)))33((x+3)12+(x)12)

= 1/((x+3)^(1/2)+(x)^(1/2))1(x+3)12+(x)12

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