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

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

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

simplify

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

- 2 + 23

Decimal Notation

2.04988 \dots

Solution steps

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

Multiply by the conjugate

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

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

Expand

(4 + 6) (2 - 3) : 2 - 23

Expand

(2 + 3) (2 - 3) : - 1

= \frac{2 - 2 3}{- 1}

\frac{2 - 2 3}{- 1} = - 2 + 23

= - 2 + 23

∣ 2 x + 3 ∣ < 6

- 7 x > 49

3 x^{2} + 22 x + 35

- 5 x > 10

5 x^{2} - x = 0

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