Question

simplify 3+√5/3-√5-3-√5/3+√5
plzz do not send any rubbish answers
if you don't know then leave it​

Answer 1

Step-by-step explanation:

3 + √5 / 3 - √5 - 3 - √5 / 3 + √5

= 3 - √5 - 3 + √5

= 3 - 3

= 0

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Answer 2

Correct question :

Simplify : $\frac{3+\sqrt{5}}{3-\sqrt{5}} -\frac{3-\sqrt{5}}{3+\sqrt{5}}$

Answer :

= 3√5

Step-by-step explanation :

  $\underline{\underline{\bf Rationalizing \ factor:}}$

=>   The factor of multiplication by which rationalization is done, is called as rationalizing factor.

=>   If the product of two surds is a rational number, then each surd is a rationalizing factor to other.

=>   For example, rationalizing factor of (3 + √2) is (3 - √2)

___________________________

$\bf =\frac{3+\sqrt{5}}{3-\sqrt{5}} -\frac{3-\sqrt{5}}{3+\sqrt{5}} \\\\\\ =(\frac{3+\sqrt{5}}{3-\sqrt{5}} \times \frac{3+\sqrt{5}}{3+\sqrt{5}})-(\frac{3-\sqrt{5}}{3+\sqrt{5}}\times \frac{3-\sqrt{5}}{3-\sqrt{5}}) \\\\\\ =\frac{(3+\sqrt{5})^2}{(3-\sqrt{5})(3+\sqrt{5})} -\frac{(3-\sqrt{5})^2}{(3+\sqrt{5})(3-\sqrt{5})} \\\\\\ =\frac{3^2+\sqrt{5}^2+2(3)(\sqrt{5})}{3^2-\sqrt{5}^2} -\frac{3^2+\sqrt{5}^2-2(3)(\sqrt{5})}{3^2-\sqrt{5}^2} \\\\\\ =\frac{9+5+6\sqrt{5}}{9-5} -\frac{9+5-6\sqrt{5}}{9-5}$

$\bf =\frac{14+6\sqrt{5}}{4} -\frac{14-6\sqrt{5}}{4} \\\\\\ =\frac{14+6\sqrt{5}-14+6\sqrt{5}}{4} \\\\\\ =\frac{12\sqrt{5}}{4} \\\\\\ =3\sqrt{5}$

_______________________________

If the question is :-

$3+\frac{\sqrt{5}}{3} -\sqrt{5}-3-\frac{\sqrt{5}}{3}+\sqrt{5}$

answer :

$= 3-3+\frac{\sqrt{5}}{3}-\frac{\sqrt{5}}{3}-\sqrt{5}+\sqrt{5} \\\\ =0$