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

The solution to rationalize 2/(7-sqrt(5)) is (7+sqrt(5))/(22)

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rationalize 2/(7-sqrt(5))

rationalize

\frac{2}{7 - 5}

\frac{7 + 5}{22}

Decimal Notation

0.41982 \dots

Solution steps

\frac{2}{7 - 5}

Multiply by the conjugate

\frac{7 + 5}{7 + 5}

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

(7 - 5) (7 + 5) = 44

= \frac{2 ( 7 + 5 )}{44}

Cancel the common factor:

2

= \frac{7 + 5}{22}

\frac{5}{3} \times \frac{2}{3}

3 \times (- 16)

3 \times (- 12)

\frac{1}{\frac{1}{x + 3} + 3}

What is rationalize 2/(7-sqrt(5)) ?
The solution to rationalize 2/(7-sqrt(5)) is (7+sqrt(5))/(22)