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}

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}

2 \frac{3}{4} \cdot 2

\frac{x + 4}{x ^{2} + 6 x + 8}

(12 x^{2} y)^{0}

\frac{4}{5 + 2}

\frac{5}{6} \div \frac{3}{10}