What is (5+2sqrt(3))/(4-sqrt(3)) ?

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

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simplify (5+2sqrt(3))/(4-sqrt(3))

simplify

\frac{5 + 2 3}{4 - 3}

2 + 3

Solution steps

\frac{5 + 2 3}{4 - 3}

Multiply by the conjugate

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

= \frac{( 5 + 2 3 ) ( 4 + 3 )}{( 4 - 3 ) ( 4 + 3 )}

Expand

(5 + 23) (4 + 3) : 26 + 133

Expand

(4 - 3) (4 + 3) : 13

= \frac{26 + 13 3}{13}

Factor out common term

13 : 13 (2 + 3)

= \frac{13 ( 2 + 3 )}{13}

Cancel the common factor:

13

= 2 + 3

- 4^{5}

(x + 1) (x + 8)

- x^{2} + x^{2}

y^{1}

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

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