How do you simplify #(3+6sqrt3) / (5 + 12sqrt3)#?

1 Answer
Jan 18, 2017

Answer:

#"3 + 6√3"/"5 + 12√3" = "(201 + 6√3)"/"407"#

Explanation:

#"3 + 6√3"/"5 + 12√3"#

Rationalising the denominator

#"3 + 6√3"/"5 + 12√3" × "5 - 12√3"/"5 - 12√3"#

#"(3 + 6√3)(5 - 12√3)"/"(5 + 12√3)(5 - 12√3)"#

#"(3)(5) - (3)(12√3) + (6√3)(5) - (6√3)(12√3)"/((5)^2 - (12√3)^2#

#"15 - 36√3 + 30√3 - 216"/"25 - 432"#

#"-201 - 6√3"/"-407"#

#"-(201 + 6√3)"/"-407"#

#"(201 + 6√3)"/"407"#