What is (2sqrt(3)-3)/(6-sqrt(3)) ?

The solution to (2sqrt(3)-3)/(6-sqrt(3)) is (3sqrt(3)-4)/(11)

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simplify (2sqrt(3)-3)/(6-sqrt(3))

simplify

\frac{2 3 - 3}{6 - 3}

\frac{3 3 - 4}{11}

Decimal Notation

0.10874 \dots

Solution steps

\frac{2 3 - 3}{6 - 3}

Multiply by the conjugate

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

= \frac{( 2 3 - 3 ) ( 6 + 3 )}{( 6 - 3 ) ( 6 + 3 )}

Expand

(23 - 3) (6 + 3) : 93 - 12

Expand

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

= \frac{9 3 - 12}{33}

Factor out common term

3 : 3 (33 - 4)

= \frac{3 ( 3 3 - 4 )}{33}

Factor the number:

33 = 3 \cdot 11

= \frac{3 ( 3 3 - 4 )}{3 \cdot 11}

Cancel the common factor:

3

= \frac{3 3 - 4}{11}

\frac{12 x ^{3} + 12 x ^{2}}{x ^{4} - x ^{2}}

175 \div 25

(5 x + 1)^{2}

\frac{7}{5} + 1

\frac{7}{35}

What is (2sqrt(3)-3)/(6-sqrt(3)) ?
The solution to (2sqrt(3)-3)/(6-sqrt(3)) is (3sqrt(3)-4)/(11)