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

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

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simplify (3sqrt(7)-5)/(sqrt(7)-2)

simplify

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

\frac{11 + 7}{3}

Decimal

4.54858 \dots

Solution steps

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

Multiply by the conjugate

\frac{7 + 2}{7 + 2}

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

Expand

(37 - 5) (7 + 2) : 11 + 7

Expand

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

= \frac{11 + 7}{3}

(\frac{1}{3})^{- (\frac{1}{3})^{- 1}}

\frac{( 6 x ^{3} + 11 x ^{2} - 47 x + 20 )}{( 2 x ^{2} + 7 x - 4 )}

2 x^{2} + 6 x + 2

- 2 \cdot 2 x

\frac{x + y}{x y} - \frac{x + 2 y}{x y + y ^{2}} - \frac{y}{x ^{2} + x y}

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