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

The solution to 5/(3-4sqrt(3)) is -(15+20sqrt(3))/(39)

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simplify 5/(3-4sqrt(3))

simplify

\frac{5}{3 - 4 3}

- \frac{15 + 20 3}{39}

Decimal Notation

- 1.27284 \dots

Solution steps

\frac{5}{3 - 4 3}

Multiply by the conjugate

\frac{3 + 4 3}{3 + 4 3}

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

Expand

5 (3 + 43) : 15 + 203

Expand

(3 - 43) (3 + 43) : - 39

= \frac{15 + 20 3}{- 39}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{15 + 20 3}{39}

64 a^{5} b^{6}

(2 r - 1) (r + 5)

4^{2} + 1 1^{2}

6 x^{3} - 6 x^{3} + 13 x^{3} - 2 x^{3}

(2 r + 3) (2 r - 3)