What is (3+5sqrt(7))/(3-sqrt(7)) ?

The solution to (3+5sqrt(7))/(3-sqrt(7)) is 22+9sqrt(7)

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simplify (3+5sqrt(7))/(3-sqrt(7))

simplify

\frac{3 + 5 7}{3 - 7}

22 + 97

Decimal Notation

45.81176 \dots

Solution steps

\frac{3 + 5 7}{3 - 7}

Multiply by the conjugate

\frac{3 + 7}{3 + 7}

= \frac{( 3 + 5 7 ) ( 3 + 7 )}{( 3 - 7 ) ( 3 + 7 )}

Expand

(3 + 57) (3 + 7) : 44 + 187

Expand

(3 - 7) (3 + 7) : 2

= \frac{44 + 18 7}{2}

Factor out common term

2 : 2 (22 + 97)

= \frac{2 ( 22 + 9 7 )}{2}

Cancel the common factor:

2

= 22 + 97

6 a^{3} + 32 a b^{2}

a + \frac{1}{b + \frac{1}{c + \frac{1}{d}}}

5 x^{2} + 6 x + 3 = 0

6 x^{2} - 5 x - 1

(- 3)^{2}

What is (3+5sqrt(7))/(3-sqrt(7)) ?
The solution to (3+5sqrt(7))/(3-sqrt(7)) is 22+9sqrt(7)