How do you rationalize the denominator and simplify 1/(sqrt5-3)1√5−3?

1 Answer
Hubert
May 3, 2016

1/(sqrt(5)-3)=-(sqrt(5)+3)/41√5−3=−√5+34

Explanation:

For expressions text(something)/(sqrt(a)-b)something√a−b we multiply the numerator and denominator by sqrt(a)+b√a+b so it matches the LHS of the formula (x+y)(x-y)=x^2-y^2(x+y)(x−y)=x2−y2.

1/(sqrt(5)-3)=1/(sqrt(5)-3) * (sqrt(5)+3)/(sqrt(5)+3)=(sqrt(5)+3)/(5-9)=-(sqrt(5)+3)/41√5−3=1√5−3⋅√5+3√5+3=√5+35−9=−√5+34

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