What is (3sqrt(6)+5sqrt(2))/(4sqrt(6)-3\sqrt{2)} ?

The solution to (3sqrt(6)+5sqrt(2))/(4sqrt(6)-3\sqrt{2)} is (51+29sqrt(3))/(39)

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simplify (3sqrt(6)+5sqrt(2))/(4sqrt(6)-3\sqrt{2)}

simplify

\frac{3 6 + 5 2}{4 6 - 3 2}

\frac{51 + 29 3}{39}

Decimal Notation

2.59562 \dots

Solution steps

\frac{3 6 + 5 2}{4 6 - 3 2}

Multiply by the conjugate

\frac{4 6 + 3 2}{4 6 + 3 2}

= \frac{( 3 6 + 5 2 ) ( 4 6 + 3 2 )}{( 4 6 - 3 2 ) ( 4 6 + 3 2 )}

Expand

(36 + 52) (46 + 32) : 102 + 583

Expand

(46 - 32) (46 + 32) : 78

= \frac{102 + 58 3}{78}

Factor out common term

2 : 2 (51 + 293)

= \frac{2 ( 51 + 29 3 )}{78}

Factor the number:

78 = 2 \cdot 39

= \frac{2 ( 51 + 29 3 )}{2 \cdot 39}

Cancel the common factor:

2

= \frac{51 + 29 3}{39}

3 (4 + 12 x) - 6 (2 x + 3) = 36 + 2 (3 x + 2)

x^{2} - 100 \geq 0

∣ y - 5 ∣ > 3

8 a - 15 = - 3

4 x^{3} + 7 x^{2} - 2 x > 0

What is (3sqrt(6)+5sqrt(2))/(4sqrt(6)-3\sqrt{2)} ?
The solution to (3sqrt(6)+5sqrt(2))/(4sqrt(6)-3\sqrt{2)} is (51+29sqrt(3))/(39)