How do you rationalize the denominator and simplify $1/(7-sqrt6)$ ?

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Answer 1 · 2016-04-02T17:44:22

$= ( 7 +sqrt6) /43$

$1 / (7 - sqrt6)$

We rationalise by multiplying the expression by the conjugate of the denominator, which is $color(blue)(7 +sqrt6$

$= (1 * color(blue)(( 7 +sqrt6))) /( (7 - sqrt6) * color(blue)( 7 +sqrt6)$

$= ( 7 +sqrt6) /( (7 - sqrt6) *( color(blue)( 7 +sqrt6))$

$= ( 7 +sqrt6) /( (7^2 - (sqrt6)^2)$

$= ( 7 +sqrt6) /( (49 - 6)$

$= ( 7 +sqrt6) /43$

How do you rationalize the denominator and simplify 1/(7-sqrt6)1/(7-sqrt6)?