What is 4/(5-sqrt(3)) ?

The solution to 4/(5-sqrt(3)) is (2(5+sqrt(3)))/(11)

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simplify 4/(5-sqrt(3))

simplify

\frac{4}{5 - 3}

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

Decimal Notation

1.22400 \dots

Solution steps

\frac{4}{5 - 3}

Multiply by the conjugate

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

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

Expand

4 (5 + 3) : 20 + 43

Expand

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

= \frac{20 + 4 3}{22}

Factor out common term

4 : 4 (5 + 3)

= \frac{4 ( 5 + 3 )}{22}

Factor the number:

4 = 2 \cdot 2

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

Factor the number:

22 = 2 \cdot 11

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

Cancel the common factor:

2

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

\frac{5 x + 1}{2} = 4 x - 7

a^{4} b^{4} - 2 a^{2} b^{2} - 99

∣ 4 (x - 1) + 2 ∣ \leq 22

\frac{18 !}{9 ! \cdot 9 !}

44 x - 121 y