What is (3-sqrt(3))/(6-sqrt(3)) ?

The solution to (3-sqrt(3))/(6-sqrt(3)) is (5-sqrt(3))/(11)

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simplify (3-sqrt(3))/(6-sqrt(3))

simplify

\frac{3 - 3}{6 - 3}

\frac{5 - 3}{11}

Solution steps

\frac{3 - 3}{6 - 3}

Multiply by the conjugate

\frac{6 + 3}{6 + 3}

= \frac{( 3 - 3 ) ( 6 + 3 )}{( 6 - 3 ) ( 6 + 3 )}

Expand

(3 - 3) (6 + 3) : 15 - 33

Expand

(6 - 3) (6 + 3) : 33

= \frac{15 - 3 3}{33}

Factor out common term

3 : 3 (5 - 3)

= \frac{3 ( 5 - 3 )}{33}

Factor the number:

33 = 3 \cdot 11

= \frac{3 ( 5 - 3 )}{3 \cdot 11}

Cancel the common factor:

3

= \frac{5 - 3}{11}

\frac{1}{2 ^{5}} \cdot \frac{1}{2 ^{7}}

lo g_{x} (81)

\frac{a ^{2}}{4}

(8 + 3 i) (2 + 5 i)

\frac{a ^{- 2}}{a ^{0}}

What is (3-sqrt(3))/(6-sqrt(3)) ?
The solution to (3-sqrt(3))/(6-sqrt(3)) is (5-sqrt(3))/(11)