What is 5/(sqrt(6)-1) ?

The solution to 5/(sqrt(6)-1) is sqrt(6)+1

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simplify 5/(sqrt(6)-1)

simplify

\frac{5}{6 - 1}

6 + 1

Decimal Notation

3.44948 \dots

Solution steps

\frac{5}{6 - 1}

Multiply by the conjugate

\frac{6 + 1}{6 + 1}

= \frac{5 ( 6 + 1 )}{( 6 - 1 ) ( 6 + 1 )}

Expand

5 (6 + 1) : 56 + 5

Expand

(6 - 1) (6 + 1) : 5

= \frac{5 6 + 5}{5}

Factor out common term

5 : 5 (6 + 1)

= \frac{5 ( 6 + 1 )}{5}

Cancel the common factor:

5

= 6 + 1

- 27 + 57 - 87 + 37 - 57 + 77

\frac{45}{360}

10 - (- 3)

64 g^{3} - 1

20 m^{9}