What is 2/(5-sqrt(3)) ?

The solution to 2/(5-sqrt(3)) is (5+sqrt(3))/(11)

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simplify 2/(5-sqrt(3))

simplify

\frac{2}{5 - 3}

\frac{5 + 3}{11}

Decimal Notation

0.61200 \dots

Solution steps

\frac{2}{5 - 3}

Multiply by the conjugate

\frac{5 + 3}{5 + 3}

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

Expand

2 (5 + 3) : 10 + 23

Expand

(5 - 3) (5 + 3) : 22

= \frac{10 + 2 3}{22}

Factor out common term

2 : 2 (5 + 3)

= \frac{2 ( 5 + 3 )}{22}

Factor the number:

22 = 2 \cdot 11

= \frac{2 ( 5 + 3 )}{2 \cdot 11}

Cancel the common factor:

2

= \frac{5 + 3}{11}

2 i \cdot (- 2) i

(x + 3) (x + 9)

x^{3} (- x^{2}) (2 x)^{3}

\frac{x ^{2} + 5 x}{x ^{2} - 25} \cdot \frac{8 x - 40}{4 x}

(2 x + 9) (3 x - 5)