Question

1/(2 - sqrt(3)) - 1/(sqrt(3) + sqrt(2)) + 5/(3 - sqrt(2))​

Answer 1

Given :    $\dfrac{1}{2-\sqrt{3} } -\dfrac{1}{\sqrt{3}+\sqrt{2} }+\dfrac{5}{3-\sqrt{2} }$

To find : Simplify

Solution:

 $\dfrac{1}{2-\sqrt{3} } -\dfrac{1}{\sqrt{3}+\sqrt{2} }+\dfrac{5}{3-\sqrt{2} }$

Let simplify each term by rationalization one by one

 $\dfrac{1}{2-\sqrt{3} } \times \dfrac{2+\sqrt{3}}{2+\sqrt{3} }=2+\sqrt{3}$

 $\dfrac{1}{\sqrt{3}+\sqrt{2} } \times \dfrac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2} } =\sqrt{3}-\sqrt{2}$

 $\dfrac{5}{3-\sqrt{2} } \times \dfrac{3+\sqrt{2} }{3+\sqrt{2} } =3+\sqrt{2}$

 $\dfrac{1}{2-\sqrt{3} } -\dfrac{1}{\sqrt{3}+\sqrt{2} }+\dfrac{5}{3-\sqrt{2} }$

= 2 + √3  - ( √3 - √2)  +  3 + √2

= 2 + √2 +  3 + √2

= 5 + 2√2

$\dfrac{1}{2-\sqrt{3} } -\dfrac{1}{\sqrt{3}+\sqrt{2} }+\dfrac{5}{3-\sqrt{2} }$   = 5 + 2√2

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(a) Rationalize the denominator: 14/ 5√3 − √5 Please Send solutions

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Answer 2

Answer:

first rationalise

after rationalise another one

then soon getting answers substitution the values

the answer is readey