What is 5/(sqrt(35)-5) ?

The solution to 5/(sqrt(35)-5) is (sqrt(35)+5)/2

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simplify 5/(sqrt(35)-5)

simplify

\frac{5}{35 - 5}

\frac{35 + 5}{2}

Decimal Notation

5.45803 \dots

Solution steps

\frac{5}{35 - 5}

Multiply by the conjugate

\frac{35 + 5}{35 + 5}

= \frac{5 ( 35 + 5 )}{( 35 - 5 ) ( 35 + 5 )}

Expand

5 (35 + 5) : 535 + 25

Expand

(35 - 5) (35 + 5) : 10

= \frac{5 35 + 25}{10}

Factor out common term

5 : 5 (35 + 5)

= \frac{5 ( 35 + 5 )}{10}

Factor the number:

10 = 5 \cdot 2

= \frac{5 ( 35 + 5 )}{5 \cdot 2}

Cancel the common factor:

5

= \frac{35 + 5}{2}

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