How do you rationalize the denominator and simplify $(4-2sqrt5)/(6-5sqrt5)$ ?

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Answer 1 · 2016-03-27T12:44:32

$(26-8sqrt5)/89$

Multiply the numerator and the denominator by the conjugate $6+5sqrt5$ of the denominator.

Use $(a-b)(a+b)=(a^2-b^2)$ to simplify the denominator.

Expand the product in the numerator.

The ratio simplifies to $(26-8sqrt5)/89$

How do you rationalize the denominator and simplify (4-2sqrt5)/(6-5sqrt5)(4-2sqrt5)/(6-5sqrt5)?