Respuesta :

Let's see what to do buddy...

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To do this, we have to multiply the face and denominator of the fraction by the denominator conjunction, which is :

[tex](5 -\sqrt{2}) [/tex]

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Reminder :

[tex](a + b)(a - b) = {a}^{2} - {b}^{2} \\ [/tex]

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So we have :

[tex] \frac{1}{ 5-\sqrt{2} } \times \frac{ 5+\sqrt{2} }{ 5 +\sqrt{2} } = \frac{1 \times ( 5 +\sqrt{2}) }{(5- \sqrt{2} )( 5 +\sqrt{2}) } = \\ [/tex]

The other is in the photo.

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And we're done.

Thanks for watching buddy good luck.

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Ver imagen hnori22003

Answer:

⇛(5+√2)/23.

Step-by-step explanation:

Given,

1/(5-√2)

The denominator is 5-√2.

We know that

The rationalising factor of a+√b is a-√b.

Therefore, the rationalising factor of 5-√2 is 5+√2. To rationalise the denominator is 1/(5-√2), we multiply this by (5+√2)/(5+√2).

∴ 1/(5-√2)

= {1/(5-√2)}×{(5+√2)/(5+√2)}

= {1(5+√2)}/{(5)²-(√2)²} [(a-b)(a+b)=-b²]

= {1(5+√2)}/{(5*5)-(√2*2)}

= {1(5+√2)}/25 - 2

= {1(5+√2)}/23

= (5+√2)/23

Hence the denominator is rationalised.

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