What is 2/(7-sqrt(3)) ?

The solution to 2/(7-sqrt(3)) is (7+sqrt(3))/(23)

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simplify 2/(7-sqrt(3))

simplify

\frac{2}{7 - 3}

\frac{7 + 3}{23}

Solution steps

\frac{2}{7 - 3}

Multiply by the conjugate

\frac{7 + 3}{7 + 3}

= \frac{2 ( 7 + 3 )}{( 7 - 3 ) ( 7 + 3 )}

Expand

2 (7 + 3) : 14 + 23

Expand

(7 - 3) (7 + 3) : 46

= \frac{14 + 2 3}{46}

Factor out common term

2 : 2 (7 + 3)

= \frac{2 ( 7 + 3 )}{46}

Factor the number:

46 = 2 \cdot 23

= \frac{2 ( 7 + 3 )}{2 \cdot 23}

Cancel the common factor:

2

= \frac{7 + 3}{23}

\frac{1}{2} x^{3} - 4 x^{2} + 3 x - 5

3 - 48

x i - x

- \frac{3 x - \frac{3}{15}}{11} + 1

3 \times + 12