What is factor (3-sqrt(7))/(5+2sqrt(7)) ?

The solution to factor (3-sqrt(7))/(5+2sqrt(7)) is (11sqrt(7)-29)/3

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factor (3-sqrt(7))/(5+2sqrt(7))

factor

\frac{3 - 7}{5 + 2 7}

\frac{11 7 - 29}{3}

Decimal Notation

0.03442 \dots

Solution steps

\frac{3 - 7}{5 + 2 7}

Multiply by the conjugate

\frac{5 - 2 7}{5 - 2 7}

= \frac{( 3 - 7 ) ( 5 - 2 7 )}{( 5 + 2 7 ) ( 5 - 2 7 )}

(3 - 7) (5 - 27) = 29 - 117

(5 + 27) (5 - 27) = - 3

= \frac{29 - 11 7}{- 3}

Apply the fraction rule:

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

29 - 117 = - (117 - 29)

= \frac{11 7 - 29}{3}

\frac{4}{4 5}

x \frac{3}{2} = 27

7 x^{2} = 5

x^{2} + 11 x y - 12 y^{2}

4 x^{2} - 7 x - 15

What is factor (3-sqrt(7))/(5+2sqrt(7)) ?
The solution to factor (3-sqrt(7))/(5+2sqrt(7)) is (11sqrt(7)-29)/3